# B.Sc. DEGREE EXAMINATION  –  STATISTICS

First SEMESTER  – NOVEMBER 2003

# ST 1500/ STA  500  STATISTICAL  METHODS

07.11.2003                                                                                        Max: 100 Marks

9.00 – 12.00

section A

Answer ALL questions                                                            (10 ´ 2 = 20 Marks)

1. Give the definition of statistics according to Croxton and Cowden.
2. Comment on the following: “ Sample surreys are more advantageous than census”.
3. Give an example for

(i) Quantitative continuous data     (ii)  Discrete time series data

1. Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
2. Mention any two limitations of geometric mean.
3. From the following results obtained from a group of observations, find the standard deviation. S(X-5) = 8 ;  S(X-5)2 = 40;  N = 20.

1. For a moderately skewed unimodal distribution, the A.M. is 200, the C.V.

is 8 and the  Karl Pearson’s coefficient of skewness is 0.3.  Find the mode

of the distribution.

1. Given below are the lines of regression of two series X an Y.

5X-6Y + 90 = 0

#### 15X -8Y-130 = 0

Find the values of .

1. Write the normal equations for fitting a second degree parabola.
2. Find the remaining class frequencies, given (AB) = 400;

(A) = 800; N=2500; (B) = 1600.

### SECTION – B

Answer any FIVE questions.                                                   (5 ´8 = 40 Marks)

1. Explain any four methods of collecting primary data.
2. Draw a histogram and frequency polygon for the following data.
 Variable Frequency Variable Frequency 100-110 11 140-150 33 110-120 28 150-160 20 120-130 36 160-170 8 130-140 49

Also determine the value of mode from the histogram.

1. Calculate arithmetic mean, median and mode from the following

frequency distribution.

 Variable Frequency variable Frequency 10-13 8 25-28 54 13-16 15 28-31 36 16-19 27 31-34 18 19-22 51 34-37 9 22-25 75 37-40 7

1. The number of workers employed, the mean wages (in Rs.) per month and standard deviation (in Rs.) in each section of a factory are given below. Calculate the mean wages and standard deviation of all the workers taken together.

 Section No. of workers employed Mean Wages (in Rs.) Standard  deviation (in Rs.) A 50 1113 60 B 60 1120 70 C 90 1115 80

1. Calculate Bowley’s coefficient of skewness from the following data.

 Variable frequency 0-10 12 10-20 16 20 -30 26 30- 40 38 40 -50 22 50-60 15 60- 70 7 70 -80 4

1. Calculate Karl Person’s coefficient of correlation from the following data.
 X 44 46 46 48 52 54 54 56 60 60 Y 36 40 42 40 42 44 46 48 50 52

1. Explain the concept of regression with an example.
2. The sales of a company for the years 1990 to 1996 are given below:

 Year 1990 1991 1992 1993 1994 1995 1996 Sales (in lakhs of  rupees) 32 47 65 88 132 190 275

Fit an equation of the from Y = abfor the above data and estimate the

sales for the year 1997.

SECTION C

Answer any TWO questions.                                                   (2 ´ 20 = 40 Marks)

1. a) Explain (i) Judgement sampling (ii) Quota sampling and

(iii) Systematic sampling methods with examples.

1. (i) Draw a blank table to show the distribution of personnel  in a

manufacturing concern according to :

• Sex: Males and Females.
• Salary grade: Below Rs.5,000; Rs.5,000 -10,000;

Rs.10,000 and above.

• Years: 1999 and 2000
• Age groups: Below 25, 25 and under 40, 40 and above

(ii) Draw a multiple bar diagram for the following data:

 Year Sales (in’000Rs.) Gross Profit Net profit 1992 120 40 20 1993 135 45 30 1994 140 55 35 1995 150 60 40

(10+5+5)

1. a) (i)  An incomplete distribution is given below

 Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 10 20 f1 40 f2 25 15

##### Given the median value is 35 and the total frequency is 170, find

the missing frequencies f1 and f2.

• Calculate the value of mode for the following data:
 Marks 10 15 20 25 30 35 40 Frequency 8 12 36 35 28 18 9

1. b) Explain any two measures of dispersion.                                       (7+7+6)
2. a) The scores of two batsman A and B is 10 innings during a certain season are:

 A 32 28 47 63 71 39 10 60 96 14 B 19 31 48 53 67 90 10 62 40 80

Find which of the two batsmen is consistent in scoring.

1. Calculate the first four central moments and coefficient of skewness from the

following distribution.

 Variable frequency Variable Frequency 25-30 2 45-50 25 30-35 8 50-55 16 35-40 18 55-60 7 40-45 27 60-65 2

(10+10)

1. a) From the following data obtain the two regression equations and calculate

the correlation coefficient.

 X 60 62 65 70 72 48 53 73 65 82 Y 68 60 62 80 85 40 52 62 60 81

1. b) (i)   Explain the concept of Kurtosis.

(ii)   In a co-educational institution, out of 200 students 150 were boys.

They took an examination and it was found that 120 passed, 10 girls

had failed. Is there any association between gender and success in the

examination?                                                                 (10+5+5)

Go To Main page

## Loyola College B.Sc. Statistics April 2004 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

# ST 1500/STA 500 – STATISTICAL METHODS

17.04.2004                                                                                                           Max:100 marks

9.00 – 12.00

SECTION -A

Answer ALL questions.                                                                               (10 ´ 2 = 20 marks)

1. Give an example for primary and secondary data.
2. What is meant by judgement sampling?
3. Mention the difference between histogram and bar diagram?
4. What are the characteristics of a good measure of central tendency?
5. For a frequency distribution, the mean and mode were found to be 15 and 24 respectively. Find the median of the distribution.
6. Comment on the following: “The mean deviation of a frequency distribution about an origin is minimum, when the origin is the mean”.
7. Define: Skewness
8. Give an example for positive correlation.
9. Find the regression equation of y on x given the following information:
10. Check the consistency of the following data:
• = 400;  (AB) = 250;     (B) = 550;       N = 1,200.

SECTION – B

Answer any FIVE questions.                                                                                     (5 ´ 8 = 40 marks)

1. Explain the different types of classification with examples.

1. The following data relate to the monthly expenditure of two families A and B:
 Items of expenditure Expenditure (in Rs.) Family A Family B Food 1600 1200 Clothing 800 600 Rent 600 500 Fuel 200 100 Miscellaneous 800 600

Represent the above data by a percentage bar diagram.

1. Calculate Q1, Q2, P3 and P20 from the following data:

Class Interval: 0-5      5-10     10-15   15-20   20-25

Frequency     :   7        18         25        30         20

1. Calculate mean deviation about median and its coefficient from the following data:

 Class Frequency Class Frequency 0-10 5 40-50 20 10-20 8 50-60 14 20-30 12 60-70 12 30-40 15 70-80 6

1. Explain the concepts of correlation and regression through an example.

1. Ten competitors in a beauty contest are ranked by 3 judges in the following order:

Judge 1:          1          6          5          10        3            2        4            9        7          8

Judge 2:          3          5          8            4        7          10        2            1        6          9

Judge 3:          6          4          9            8        1            2        3          10        5          7

Use the rank correlation coefficient to determine which pair of judges has the nearest approach to common tastes in beauty.

1. Find Yule’s coefficient of association between literacy and unemployment from the following data:

Literate:                         1,290

Unemployed:                1,390

Literate unemployed:       820

1. Fit a straight line trend for the following time series.

Year           :    1990    1991    1992    1993    1994    1995    1996

Production

of steel

(in tonnes) :       60      72         75        65        80        85        95

Estimate the production for the year 1997.

SECTION – C

Answer any TWO questions                                                                        (2 ´ 20 = 40 marks)

1. i) Explain the various method of collecting primary data.
2. ii) Draw ‘less than’ and ‘more than’ Ogive curves for the following data:
 Profit (in lakh) Number of Companies Profit (in lakh) Number of companies 10-20 6 60-70 16 20-30 8 70-80 8 30-40 12 80-90 5 40-50 18 90-100 2 50-60 25

Also find the value of the median.                                                                            (10+10)

1. i) Calculate mode ( by grouping method) from the following data:

Class interva l: 10-20  20-30   30-40   40-50   50-60   60-70   70-80   80-90

Frequency     :      5         9         13        21        20        15         8         3

1. ii) From the prices of shares of 2 firms X and Y given below, find out which is more stable

in value.

Firm X:            35        54        52       53       56       58        52        50        51        49

Firm Y:            108      107      105      105      106      107      104      103      104      101

(10+10)

1. i) Explain the concept of kurtosis.

1. ii) Calculate the first four central moments from the following frequency distribution.

x:         2          3          4          5          6

f:          1          3          7          3          1

iii) Calculate Karl pearson’s coefficient of correlation, for the following data and interpret

its value.

X:        48        38        17        23        44

Y:        45        20        40        25        45                                                             (5+7+8)

1. i) From the following data, obtain the regression equations of Y on X and X on Y.

Aptitude scores(X):  60    62       65        70        72        48        53        73        65        82

Productivity

Index(Y)               :   68    60       62        80        85        40        52        62        60        81

Also estimate the productivity index, when test score is 92 and the test score when productivity index is 75.

1. ii) Explain any two methods of studying the association between attributes. (15+5)

Go To Main page

## Loyola College B.Sc. Statistics Nov 2006 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 AB 01

FIRST SEMESTER – NOV 2006

# ST 1500 – STATISTICAL METHODS

(Also equivalent to STA 500)

Date & Time : 01-11-2006/1.00-4.00   Dept. No.                                                       Max. : 100 Marks

SECTION A

Answer ALL questions.                                                                 (10 x 2 =20 marks)

1. Define Statistics.
2. Distinguish between primary and secondary data.
3. What are the advantages of diagrammatic and graphic presentation of data?
4. What are the desirable properties of a good average?
5. What purpose does a measure of dispersion serve?
6. Interpret r when r = 1, -1, 0, where r is the correlation coefficient.
7. What is the purpose of regression analysis?
8. Define kurtosis.
9. How would you distinguish between association and correlation?
10. Check for consistency: (A) = 100, (B) = 150, (AB) = 60, N = 500.

SECTION B

Answer any FIVE questions.                                                          (5 x 8 =40 marks)

1. Explain the various methods that are used in the collection of primary data, pointing out their merits and demerits.

1. Represent the above frequency distribution by means of a histogram and superimpose the corresponding frequency polygon. Experience (in months).

 Experience 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 No. of Workers 5 6 15 10 5 4 2 2

1. (i) Calculate the Geometric Mean for the following values:

85, 70, 15, 75, 500, 8, 45, 250, 40, 36.

(ii) An aero plane covers four sides of a square at speeds of 10000, 2000, 3000 and 4000 Kms. per hour respectively. What is the average speed of the plane in the flight around the square?

1. Calculate Quartile deviation and coefficient of Quartile deviation from the following data:
 Wages (in Rs.) Less than 35 35-37 38-40 41-43 Over 43 No. of wage earners 14 62 99 18 7

1. Find Bowley’s coefficient of skewness for the following frequency distribution.
 X 0 1 2 3 4 5 6 Frequency 7 10 16 25 18 11 8

1. Fit a straight line to the following data.

 X 6 2 10 4 8 Y 9 11 5 8 7

1. The ranking of two students in two subjects A and B are as follows:

 A 6 5 3 10 2 4 9 7 8 1 B 3 8 4 9 1 6 10 7 5 2

Calculate rank correlation coefficient.

1. 300 people of German and French nationalities were interviewed for finding their preference

of music of their language. The following facts were gathered out of 100 German nationals,

60 liked music of their own language, whereas 70 French nationals out of 200 liked German

music. Out of 100 French nationals, 55 liked music of their own language and 35 German

nationals out of 200 Germans liked French music.  Using coefficient of association, state

whether Germans prefer their own music in comparison with Frenchmen.

SECTION C

Answer any TWO questions.                                                        (2 x 20 =40 marks)

1. (i) Define sampling and explain the different methods of sampling.

(ii) Draw an ogive for the following distribution and calculate the median wage.

 Wages 1000-1100 1100-1200 1200-1300 1300-1400 1400-1500 1500-1600 Workers 6 10 22 16 14 12

1. (i) Following are the records of two players regarding their performance in cricket matches.

Which player has scored more on an average? Which player is more consistent ?

 Player A 48 52 55 60 65 45 63 70 Player B 33 35 80 70 100 15 41 25

(ii) You are given the following data about height of boys and girls in a certain college. You are required to find out the combined mean and standard deviation of heights of boys and girls taken together.

 Number Average height Variance Boys 72 68” 9” Girls 38 91” 4”

1.  (i) Find the coefficient of correlation with the help of Karl Pearson’s method.
 10 20 30 40 50 5 2 4 1 4 1 10 8 2 5 1 – 15 – 3 2 1 – 20 – 1 3 2 4 25 – – 4 2 –

Marks in Mathematics

Marks in

Statistics

(ii) In a group of 800 students, the number of married is 320. But of 240 students who failed, 96 belonged to the married group. Find out whether the attributes marriage and failure are independent.

1. The following table gives the aptitude test scores (X) and productivity indices (Y) of 10 workers selected at random:
 X 60 62 65 70 72 48 53 73 65 82 Y 68 60 62 80 85 40 52 62 60 81

• Find the two regression equations.
• Estimate the productivity index of a worker whose test score is 92.
• Estimate the test score of a worker whose productivity index is 75.
• Using the two regression equations find the correlation coefficient.

Go To Main page

## Loyola College B.Sc. Statistics April 2007 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 AC 01

FIRST SEMESTER – APRIL 2007

# ST 1500 – STATISTICAL METHODS

Date & Time: 24/04/2007 / 1:00 – 4:00 Dept. No.                                                Max. : 100 Marks

# PART-A

1. Define statistics.
2. Explain ordinal data,nominal data.
3. State any two merits of median.
4. Find the values of Q1 and Q3 for the following data.

20,28,40,12,30,15,50

1. Write the formulas for β1 and β2 in terms of the moments.
2. Mention the properties of the correlation coefficient.
3. Given the two regression equations

8X – 10Y= – 66

40X – 18Y = 214

find the mean values of X and Y.

1. What are the normal equations for fitting

Y= abx?

1. Find whether the given data

(A)=100, (B)=150, (AB)=60,N=500 is consistent.

1. Explain scatter diagram.

PART-B

1. Draw the Box-whisker plots for the following data and compare.

Scores of jayanth   58  59  60  54  65  66   52  75   69  62

Scores of vasanth   87  89  78  71  73  84  65  66  56   46

1. Obtain the mean deviation about median for the marks give below;

Marks                                           Frequency

• 7
• 12

20-30                                                    18

30-40                                                    25

40-50                                                    16

50-60                                                    14

60-70                                                     8

1. Calculate the rank correlation coefficient for the variables X and Y  from the  following data:

X   75    88    95    70    60     80    81     50

Y  120  134  150  115  110   140  142   100

1. Fit a parabolic curve to the following time series:

Year    1997    1998    1999    2000    2001    2002    2003

Production     42         49        62        75        92      122      158

1. In a group of 800 students , the number of married is 320.But of 240 students who

failed,96 belonged to the married group.Find out whether the attributes marriage

and failure are independent.

1. Find the geometric mean for the following data given below.

Marks                        Frequency

• 6
• 10
• 18
• 30
• 15
• 12
• 10
• 6
• 2
1. An algebra test was given to 400 school children of whom 150 were boys and 250

girls.The results were as follows.

Boys                   Girls

Mean              72                       73

SD                7                       6.4

Sample size      150                     250

Find the combined mean and combined standard deviation.

1. Explain the various types of diagrams used in statistical applications.

### PART-C

1. The following table gives the aptitude test scores and productivity indices of 10

workers selected at random.

Aptitude scores(X)     60   62   65    70   72   48   53   73   65   82

Productivity

index(Y)     68   60   62    80   85   40   52   62   60   81

i)Obtain the regression equation of Y on X

ii)Obtain the regression equation of X on Y

iii)Obtain productivity index of a worker with test score=92

1. iv) Obtain the test score of a worker whose productivity index is 75

v)obtain the correlation coefficient between X and Y through regression

equations.

1. Two brands of tyres are tested with the following results.

No    of    tyres

Life(000 miles)                                        X        Y

20-25                                                 1          0

25-30                                                22        24

30-35                                                64        76

35-40                                                10         0

40-45                                                 3          0

i)Which brand of tyres has greater average life?                                    (5)

ii)Calculate coefficient of variations and state which one is consistent.            (15)

1. Find β1 and β2 for the following data and interpret the results.

Age                                    Frequency

• 2
• 8
• 18
• 27
• 25
• 16
• 7
• 2
1. a)Explain the contingency tables and the method of calculating chi-square for a

contingency table.

b)Coefficient of correlation between X and Y for 20 items is 3,mean of X is 15 and

that of Y 20,standard deviations are 4 and 5 respectively.At the time of calculation

one item 27 has wrongly been taken as 17 in case of X values and 35 instead of 30

in  case of Y series.Find the correct coefficient of correlation.

Go To Main page

## Loyola College B.Sc. Statistics April 2008 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

# NO 1

FIRST SEMESTER – APRIL 2008

# ST 1500 – STATISTICAL METHODS

Date : 03/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

(10 x 2 = 20 marks)

1. Distinguish between Census and sample.
2. State the objectives of classification of data.
3. Why do we call Arithmetic mean is a good average?
4. When do you say a distribution is skewed? Sketch positive and negative skew ness.
5. What is curve fitting?
6. Write down the normal equations for fitting .
7. If for two variable X and Y, correlation coefficient

find the regression co efficient of X onY.

1. If two regression lines are  and  for two variables X and Y, find the mean values of X and Y.
2. In a report on consumers preference, it was given that out of 500 persons surveyed 410 preferred variety A, 380 preferred variety B and 270 persons liked both. Are the data consistent?
3. State any two characteristics of Yule’s coefficient of Association.

PART – B

(5 x 8 = 40 marks)

1. Draw  ogive curves for the data given below:
 Draw Sales (Rs.000) 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of Shops 3 6 10 15 8 4 2

1. Distinguish between Classification and Tabulation.

1. Calculate Karl Pearson’s Co efficient of Skewness for the data given below. On the basis of mean, median and standard deviation.
 Wages: 5 6 7 8 9 10 11 12 Workers: 25 45 65 100 30 75 40 50

1. Bring out the relationship between to the following data:
 x: 0 1 2 3 4 y: 1 1.8 1.3 2.5 2.3

1. Fit a parabola of second degree to the following data
 x: 0 1 2 3 4 y: 1 1.8 1.3 2.5 2.3

1. What do you understand by regression? Why there are two regression equations? What are its uses?
2. From the following data, calculate the coefficient of rank correlation between X and Y
 X: 36 56 20 65 42 33 44 50 15 60 Y: 50 35 70 25 58 75 60 45 80 38

1. 1660 candidates appeared for a competitive examination. 422 were successful, 256 had attended a coaching class, and of these 150 came out successful. Estimate the utility of the coaching classes.

PART – C

(2 x 20 = 40 marks)

1. a) Calculate mean deviation from median from the following data.
 Class Interval: 20-25 25-30 30-40 40-45 45-50 50-55 Frequency: 6 12 17 30 10 10

 Class Interval: 55-60 60-70 70-80 Frequency: 8 5 2

1. b) From the prices of shares X and Y given below, state which share is more stable in value

1.  It is known that the readings for x and y given below should follow a law of the form , where a and b are constants
 x: 1 2 3 4 5 6 7 8 y: 5.43 6.28 8.23 10.32 12.63 14.86 17.27 19.51

use the method of least squares to find the best values of a and b.

1. Calculate and from the data given below
 Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No. of Students: 8 12 20 30 15 10 5

1. Calculate the two regression equations Y on X and X on Y and correlation coefficient     .
 Price (Rs): 10 12 13 12 16 15 Amount Demanded 40 38 43 45 37 43

Also estimate the likely demand when the price is Rs.20.

Go To Main page

## Loyola College B.Sc. Statistics Nov 2008 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

# BA 01

FIRST SEMESTER – November 2008

# ST 1500 – STATISTICAL METHODS

Date : 10-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A                                 (10×2=20)

1. What is a census survey?
2. Identify the scale used for each of the following variables
1. Calories consumed during the day.
2. Marital status.
3. Perceived health status reported as poor, fair, good or excellent.
4. Blood type
3. Mention any four measures of dispersion.
4. Give a measure of kurtosis.
5. State the principle of least squares.
6. What is the standard form of growth curves?
7. When will the regression lines be perpendicular to each other?
8. If the regression coefficients are b­XY­ = – 0.4 and b­YX­ = – 0.9 find the

correlation coefficient between X and Y.

1. What is a dichotomous classification?
2. State the relation between Yule’s coefficient of association and

coefficient of colligation.

PART – B                                 (5×8=40)

1. Describe any two methods of collecting primary data along with their

merits and demerits.

1. Explain the importance of diagrammatic representation of data.
2. Compute mean and median for the following frequency distribution

Sales target : 10-20     20-30     30-40     40-50     50-60

(Rs.lakhs)

No. of times

achieved  :    6             8           12             9             5

1. The sum and sum of squares corresponding to length X (in cm) and weight Y (in gms) of 50 tapioca tubers are given below:

∑X = 212, ∑X­­2 = 902.8, ∑Y = 261, ∑­Y­2 = 1457.6

Which is more varying, the length or weight?

1. Measurements of serum cholesterol (mg/100ml) and arterial calcium deposition (mg/100g dry weight of tissue) were made on 12 animals. The data are as follows:

Calcium

(X)  :  59    52    42    59    24    24    40    32    63    57    36    24

Cholesterol

(Y)  : 298  303  233  287  236  245  265  233  286  290  264  234

Calculate the correlation coefficient.

1. The equations of the two regression lines obtained in a correlation

analysis are as follows:

3X+12Y = 19, 3Y+9X = 46

Obtain i) the value of correlation coefficient.

1. ii) Mean values of X and Y.

iii) Ratio of the coefficient of variability of X to that of Y.

1. What do you understand by consistency of given data? Examine the

consistency of the following data:

N = 1000, (A) = 600, (B) = 500, (AB) = 50, the symbols having their

usual meanings.

1. In a certain investigation carried on with regard to 500 graduates and 1500 non-graduates, it was found that the number of employed graduates was 450 while the number of unemployed non-graduates was 300.

In the second investigation 5000 cases were examined. The number of

1. The number of graduates who were found to be employed was
2. Calculate the coefficient of association between graduates and

employment in both the investigations. Can any definite conclusion be

drawn from the coefficients?

PART – C                                 (2×20=40)

1. Draw a Histogram for the following frequency distribution of output produced by 190 workers in a firm and use it to find an approximate value of the mode. Also verify it using the formula.

Output in units : 300-310   310-320   320-330   330-340   340-350

No. of workers :      9              20             24            38            48

Output in units : 350-360   360-370   370-380

No. of workers :    27              17             7

1. Calculate a measure of dispersion and a measure of skewness based on quartiles from the following distribution:

Wages (Rs.): below 35    35-37    38-40    41-43    over 43

No.of wage

earners    :        14          60         95          24            7

1. Consider the following data where x is temperature (in oc) and Y is the number of eggs per cm­2 .

X   :   3        5       8        14       21      25      28

Y   : 2.8     4.9     6.7     7.6      7.2     6.1     4.7

Fit a quadratic equation to these data.

1. Various dose of a poisonous substance were given to groups of 25 mice and the following results were observed:

Dose(mg):  4      6      8      10      12      14      16

Number

of deaths:   1     3       6      8       14      16      20

Find the equation of the regression lines. Estimate the number of deaths

in a group of 25 mice who receive a 7-milligram dose of this poison.

Go To Main page

## Loyola College B.Sc. Statistics April 2009 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 YB 01

FIRST SEMESTER – April 2009

# ST 1502/ST 1500 – STATISTICAL METHODS

Date & Time: 20/04/2009 / 1:00 – 4:00  Dept. No.                                                      Max. : 100 Marks

PART – A

Answer ALL questions:                                                                                   10 x 2 = 20

1. States any two applications of statistics.
2. Distinguish between primary and secondary data.
3. What are the characteristics of a good measure of central tendency?
4. Find the coefficient of variation from the following data.

.

1. State the principle of least squares.
2. Write the normal equations for fitting the curve .
3. The ranks of two attributes in a sample are given below. Find the correlation between them.
4. If and are the regression coefficients of y on x and x on y respectively, show that.
5. Check whether A and B are independent given the data:

N=10,000,       (A)=4500,        (B)=6000,        (AB)=3150

1. Distinguish between correlation and regression.

PART – B

Answer any FIVE questions:                                                               5 x 8 = 40

1. Explain classification and tabulation of data.
2. Draw less than and more than ogives from following data:
 Profits: (Rs. Lakhs 10-20 20-30 30-40 40-50 50-60 No. of Companies: 6 8 12 18 25 Profits: (Rs. Lakhs) 60-70 70-80 80-90 90-100 No. of companies: 16 8 5 2
1. Calculate the mean, median and hence mode from the following data:
 Mid pt: 15 25 35 45 55 65 75 85 Frequency: 5 9 13 21 20 15 8 3
1. For a moderately skewed data, the arithmetic mean is 200, the coefficient of variation is 8 and Karl Pearson’s coefficient of skewness is 0.3. Find the mode and median.
2. Fit a straight line trend for the following data:
 Year: 1980 1981 1982 1983 1984 1985 1986 Y: 83 60 54 21 22 13 23
1. Show that the coeffient of correlation lies between -1 and +1.
2. In a group of 800 students, the number of married students is 320. But of 240 students who failed, 96 belonged to the married group. Find out whether the attributes of marriage and failure are independent.
3. Given the following data, find the two regression equations:

PART – C

Answer any TWO questions:                                                               2 x 20 = 40

1. a) Explain the scope and limitations of statistics.
2. b) The following table gives the frequency, according to groups of marks obtained by 67 students in an intelligence test. Calculate the degree of relationship between age and intelligence test.
 Age in years Test marks 18 19 20 21 Total 200-250 4 4 2 1 11 250-300 3 5 4 2 14 300-350 2 6 8 5 21 350-400 1 4 6 10 21 10 19 20 18 67
1. a) Define measure of dispersion. Prove that the standard deviation is independent of change of origin but not scale.
2. b) Find the coefficient of quartile deviation from the following data.
 Wages: 0-10 10-20 20-30 30-40 40-50 No.of Workers: 22 38 46 35 20
1. Calculate the first four moments about the mean and also the values of and from the following data:
 Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No. of Students: 8 12 20 30 15 10 5
1. a) Fit the curve using the principle of least squares.
2. b) From the following data, calculate the remaining frequencies and hence test whether A and B are

independent.

.

Go To Main Page

## Loyola College B.Sc. Statistics Nov 2010 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – NOVEMBER 2010

# ST 1502/ST 1500 – STATISTICAL METHODS

Date : 10-11-10                     Dept. No.                                                    Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

1. State any two limitations of statistics.
2. Write down the types of Scaling with examples.
3. Define measures of central tendency.
4. What do you mean by skewness?
5. Write down the normal equations for the exponential curve.
6. What is curve fitting?
7. State the assumptions underlying in Karlpearson’s correlation co-efficient.
8. Define probable error.
9. Examine the consistency of the following data:

N= 1000; (A)= 600; (B)= 500; (AB)= 50.

1. Write the Yule’s Coefficient of association between the attributes.

PART – B

1. Describe the various types of diagrammatic representation of data.
2. Draw the cumulative frequency curve. find the quartiles for the following data:
 Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No of Students 4 8 11 15 12 6 3

1. Find the missing frequencies using the median value 46 for the following data:
 Variable 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Total Frequency 12 30 ? 65 ? 25 18 219

1. The first of the two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation √13.44. Find the standard deviation of the second group.
2. Show that the correlation coefficient cannot exceed unity.
3. Obtain a straight line trend equation by the method of least squares. Find the value for the

missing year 1961.

 Year 1960 1962 1963 1964 1965 1966 1969 Value 140 144 160 152 168 176 180
1. Find the association of A and B in the following cases:
1. N = 1000; (A)= 470;  ( B)= 620 and (AB)= 320
2. (A)= 490; (AB)= 294; (α)= 570 and (αβ)= 380
• (AB)= 256; (αB)= 768; ( Aβ)= 48 and ( αβ)= 144.
1. Find the angle between the two regression lines.

PART – C

1. a) Describe the various types of classification and tabulation of data in detail.                              (12)

1. b) A cyclist pedals from his house to his college at a speed of 10Kmph and back from

the college to his house at 5Kmph. Find the average speed.                                                         (8)

1. a) For a distribution, the mean is 10, variance is 16, γ1 is +1 and β2 is 4. Obtain

the first four moments about the origin. Make a comment on distribution.

1. b) Calculate i) Quartile Deviation and ii) Mean Deviation from mean for the

following data:

 Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No of Students 6 5 8 15 7 6 3

1. a) The following table gives, according to age, the frequency of marks obtained by 100 students

in an intelligence test: Calculate the Correlation Coefficient.

 Age 18 19 20 21 Total Marks 10-20 4 2 2 0 8 20-30 5 4 6 4 19 30-40 6 8 10 11 35 40-50 4 4 6 8 22 50-60 0 2 4 4 10 60-70 0 2 3 1 6 Total 19 22 31 28 100

1. b) Predict the value of Y when X=6 for the following data:

Σx=55; Σxy=350; Σy=55; Σx2=385 and n=10.

1. a) Fit an exponential curve of the form Y=abx to the following data:
 X 1 2 3 4 5 6 7 8 Y 1 1.2 1.8 2.5 3.6 4.7 6.6 9.1

1.       b) 800 candidates of both sex appeared at an examination. The boys outnumbered the

girls by 15% of the total. The number of candidates who passed exceed the number

failed by 480. Equal number of boys and girls failed in the examination.

Prepare a 2×2 table and find the coefficient of association. Comment on the result.

Go To Main page

## Loyola College B.Sc. Statistics April 2011 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2011

# ST 1502/ST 1500 – STATISTICAL METHODS

Date : 19-04-2011              Dept. No.                                          Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

1. Write any two limitation of statistics.
2. What is classification?
3. Mention Various measures of central tendency.
4. Define Skewness.
5. Write the normal equations to fit a parabola by the principles of least squares.
6. Explain curve fitting.
7. Define correlation.
8. State any two properties of regression coefficients.
9. Find the missing frequencies from the following data, (A)=400,  (AB)=250, (B)=500,  N=1200.
10. Explain Yule’s coefficient of association.

PART – B

1. Explain the various types of classification of data.
2. Distinguish between primary data and secondary data.
3. Find Arithmetic mean and mode for the following data:

Profit per shop:         0-10      10-20      20-30      30-40      40-50           50-60

No. of shops   :           12         18            27            20          17               6

1. Define Kurtosis. Also explain various measures of Kurtosis.
2. Fit a straight line trend for the following data:

Year:             1994         1995           1996               1997               1998               1999

Production      7             9                12                 15                  18                  23

1. What is a scatter diagram? How does it help us in studying the correlation between two variables with respect to their nature of relationship?
2. The following table gives the age of cars of certain make and annual maintenance costs. Obtain the regression equation for costs related to age:

Age of cars in years:            2          4          6          8

Maintenance cost

in Rs. Hundreds:                10          20        25        30

1. Find out the coefficient of association from the following data:

Passed                       Failed             Total

Married                         90                                 65                 155

Unmarried                   260                             110               370

PART – C

1. a) What do you understand by Tabulation? What are the different parts of a table?

Explain.                                                                                                                               (2+8)

1. b) Draw a histogram and frequency polygon to represent the following data.

Weekly wages:         10-15              15-20              20-25              25-30              30-35              35-40

No. of workers;           7                      19                   27                    15                     12                    8                                                                                                                                                                     (7+3)

1. a) Calculate mean deviation from mean for the following data:

Class interval:     2-4      4-6      6-8      8-10

No. of person:     3         4          2          1                                                                        (3+5)

1. b) Calculate Bowley’s coefficient of Skewness from the following data:

Marks:            1-10    10-20    20-30     30-40     40-50         50-60     60-70    70-80

No. of

persons:          10         25         20          15           10            35           25         10           (12)

1. a) Write the procedure to fit a second degree parabola using method of least squares.

(6)

1. b) Fit a second degree parabola to the following.

Year ;      1978           1979               1980               1981               1982               1983

Price:       100            107                  128                140                 181                  192        (14)

1. a) Show that the coefficient of correlation lies between -1 and +1.       (10)

1. b) The following results were obtained in a survey:

Boys               Girls

No. of candidates appeared at an examination             800                200

Married                                                                                   150                   50

Married and successful                                                       70                   20

Unmarried and successful                                                 550                 110

Find the association between marital status and the success at the examination both for boys and girls.                                                                                                                                                       (10)

Go To Main page

## Loyola College B.Sc. Statistics April 2012 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2012

# ST 1502/ST 1500 – STATISTICAL METHODS

Date : 28-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL questions:                                                                                        (10 x 2 = 20 marks)

1. State any two limitations of statistics.
2. What is meant by classification?
3. Define dispersion.
4. Explain Kurtosis.
5. What is curve fitting?
6. Explain the principle of least squares.
7. Define correlation with an example.
8. State any two properties of regression coefficients.
9. Explain association of attributes.
10. Define Independence of attributes.

PART – B

Answer any FIVE questions:                                                                                        (5 x 8 = 40 marks)

1. Explain the Scope of statistics.
2. Describe Nominal and Ordinal scaling. Also write their advantages.
3. Define skewness. Explain the various measures of skewness.
4. Calculate the mean and mode for the following frequency distribution:

Monthly Wages:   Less than 200        200-400           400-600           600-800             800-100

No. of workers:              78                    165                   93                     42                        12

1. Fit a straight line trend for the following data:

Year:   1990    1991    1992    1993    1994    1995    1996

Y:         127      101      130      132      126      142      137

1. Prove that the coefficient of correlation lies between -1 and +
2. From the following data calculate the coefficient of rank correlation between x and y.

X:         36        56        20        65        42        33        44        50        15        60

Y:         50        35        70        25        58        75        60        45        80        38

1. a) Arrange the following data in a 2×2 contingency table and find the unknown class frequency,

given that the total frequency is 500:

Intelligent fathers with intelligent sons  250

Dull fathers with intelligent sons             75

Intelligent fathers with Dull sons              40

1. b) Ascertain whether there is any relationship between intelligence of fathers and sons.

(P.T.O)

PART – C

Answer any TWO questions:                                                                              (2 x 20 = 40 marks)

1. a) Explain the applications of diagrams and graphs and state their advantages.

1. b) Define Primary data. What are the sources of primary data?
2. Calculate first four moments about mean from the following data. Also calculate b1 and

b2 and comment on the nature of the distribution.

X:     0        1          2          3          4          5          6          7          8

f:      5        10        15        20        25        20        15        10        5

1. a) Fit a second degree parabola to the following data:

Year:              1982  1983    1984    1985    1986    1987    1988    1989    1990

y:     4        8          9         12        11        14        16        17        26                         (12 marks)

1. b) Calculate Karl-Pearson’s coefficient of correlation from the following data.

X:  10   12   18    24     23   27

Y:  13   18    12   25     30   10                                                                (8 marks)

1. a) Given the following data, find the two regression equations:

(8 marks)

1. b) Find the missing frequencies from each of the following two data:

(i)    (A) = 400,     (AB) = 250,    (B) = 500,      N = 1200

(ii)       (B) = 600,

Is there any inconsistency in the data given above?                                       (12 marks)

Go To Main Page

## Loyola College B.Sc. Statistics Nov 2012 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – NOVEMBER 2012

# ST 1502/ST 1500 – STATISTICAL METHODS

Date : 08/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL the questions:                                                                                       (10 x 2 = 20)

1. Why is sampling necessary under certain conditions?
2. A survey of 100 people is conducted and all are asked questions relating to the following characteristics:
• marital status
• salary
• occupation
• number of hours of television they watch per week

What type of data and measurement scales are applicable?

1. List the requisites of a good measure of central tendency.
2. What is meant by Kurtosis?
3. State the principles of least squares.
4. What is the general form of growth curves?
5. Define rank correlation coefficient.
6. Find the means of variables X and Y and the correlation coefficient given the following information:

Regression equation of Y on X:    3Y – X – 50 = 0

Regression equation of X on Y:    3Y– 2X –10 = 0

1. Out of 900 persons, 300 were literates and 400 had travelled beyond the limits of their district.100 of the literates were among those who had not travelled. Is there any relation between literacy and travelling?
2. What is meant by coefficient of colligation?

PART – B

Answer any FIVE questions:                                                                           (5 x 8 = 40 marks)

1. The survey about colour preferences reported the age distribution of the people who responded.
 Age group (years) 1-18 19-24 25-35 36-50 51-69 70-74 count 10 97 70 36 14 5

Draw ‘less than ogive’ curve and locate the median.

1. Describe the various ways of classification of statistical data with suitable illustrations.
2. The volumes of water (in litres) consumed by 12 elephants in one day are listed below:

66        90        68        94        86        96        70        138      90        120      92        102

Calculate the mean and variance and interpret the data.

1. Describe the construction of Lorenz curve.
2. What is skewness? Distinguish diagrammatically the different types of skewness.
3. Calculate the sample coefficient of correlation between number of ovulated follicles

and number of eggs laid by pheasants. Data of 11 pheasants were collected:

 Number of eggs 39 29 46 28 31 25 49 57 51 21 42 Number of follicles 37 34 52 26 32 25 55 65 40 25 45

1. Fit a curve of the form y = abt for the following data observed on the growth of a fruitfly population
 Time t (in days) 2 3 4 5 6 7 8 9 No.of flies y 110 116 122 128 134 141 148 155
1. Describe the conditions for consistency of data when there are three attributes.

PART – C

Answer any TWO questions                                                                                 (2 x 20 = 40 marks)

1. (a) What is meant by a questionnaire? Explain the precautions that must be taken

while drafting a questionnaire.                                                                             (12 marks)

(b) Distinguish between primary and secondary data.                                               (8 marks)

1. (a) Establish the relationship between raw and central moments.                              (10 marks)

(b) The following frequency distribution is the weight in pounds of 57 children at a

day-care center:

 Weight (in pounds) 10-19 20-29 30-39 40-49 50-59 60-69 70-79 No. of children 5 19 10 13 4 4 2

Calculate mean deviation about median.                                                               (10 marks)

1. (a) What is meant by ‘curve fitting’? Give the normal equations to fit a second degree

parabola.                                                                                                                (10 marks)

(b) In a sample of 500 children, 200 came from higher income group and the rest

from lower income group. The numbers of delinquent c hildren in these groups

were 25 and 100 respectively. Calculate the coefficient of association between

delinquency and income group.                                                                            (10 marks)

1. Potato chip lovers do not like soggy chips,so it is important to find characteristics of the production process that produce chips with an appealing texture. The following sample data on frying time(in seconds) and moisture content(%) were selected.
 Frying time 65 50 35 30 20 15 10 5 Moisture content 1.4 1.9 3 3.4 4.2 8.1 9.7 16.3

Predict the moisture content of the chips if the frying time is 40 seconds.

Go To Main Page

## Loyola College B.Sc. Computer Science Nov 2006 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

 AK 05

THIRD SEMESTER – NOV 2006

# CS 3201 – STATISTICAL METHODS

Date & Time : 31-10-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

SECTION A

Answer ALL the questions.                                                                                10 × 2 = 20

1. Define Geometric Mean.
2. Find the mode for the following distribution:

Class interval:  0-10     10-20   20-30   30-40   40-50   50-60   60-70

Frequency     :    5            8          7         12       28         20        10

1. State the properties of regression lines.
2. Write the application of chi-square test.
3. Three coins are tossed. What is the probability of getting at least one head?
4. What is the chance that a leap year selected at random will contain 53 Sundays?
5. Find the expectation of the number on a die when thrown.
6. If X and Y are two random variables, determine whether X and Y are independent for the following joint probability density function

.

1. Find the moment generating function of Uniform distribution.
2. Write the probability density function of Normal distribution.

SECTION B

Answer ALL the questions.                                                                                  5 × 8 = 40

1. (a) Calculate the mean and median for the following frequency distribution.

Class interval:  0-8       8-16     16-24   24-32   32-40   40-48

Frequency     :   8           7          16        24         15        7

(or)

(b) Calculate the (i) Quartile deviation and (ii) Mean deviation from mean for the               following data.

Marks              :           0-10     10-20   20-30   30-40   40-50   50-60   60-70

No of students :            6            5          8          15       7           6          3

1. (a) A problem in Statistics is given to five students whose chances of solving it are 1/6, 1/5, 1/4, 1/3 and 1/2 respectively. What is the probability that the problem is solved?

(or)

(b) A coin is tossed three times. Find the chances of throwing, (i) three heads (ii) two heads and one tail and (iii) head and tail alternatively.

1. (a) A computer while calculating correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results : n = 25, ∑X = 125, ∑= 650, ∑Y = 100, ∑= 460, ∑XY = 508. It was however later discovered at the time of checking that he had copied down tow pairs as while the correct values are. Obtain the correct value of correlation coefficient.

(or)

(b) A random sample of students of XYZ University was selected and asked their opinion about ‘autonomous colleges’. The results are given below. The same number of each sex was included within each class-group. Test the hypothesis at 5% level that opinions are independent of the class groupings. (Given value of chi-square for 2, 3 degree of freedom are 5.991, 7.82 respectively)

 class Favouring ‘autonomous colleges’ Opposed to ‘autonomous colleges’ B.A/B.Sc part I 120 80 B.A/B.Sc part II 130 70 B.A/B.Sc part III 70 30 M.A/M.Sc. 80 20

1. (a) For the discrete joint distribution of two dimensional random variable (X, Y) given below, calculate E(X), E(Y), E(X+Y), E(XY). Examine the independence of variables X and Y.
 X  \  Y 2 5 -1 0.27 0 0 0.08 0.04 2 0.16 0.1 3 0 0.35

(or)

(b) A random variable X has the following probability function:

X   : 0        1          2          3          4          5          6          7

P(X)    : 0  k          2k        2k        3k

(i) Find k (ii) Evaluate P(X<6),  and  (iii) determine the distribution function of X.

1. (a) A coffee connoisseur claims that he can distinguish between a cup of instant coffee and a cup of percolator coffee 75% of the time. It is agreed that his claim will be accepted if he correctly identified at least 5 of the 6 cups. Find his chance of having the claim (i) accepted (ii) rejected when he does have the ability he claims.

(or)

(b) Define Exponential distribution. Find the mean and variance of the same.

SECTION C

Answer any TWO questions:                                                                              2 × 20 = 40

1. (a) The first four moments of a distribution about the value 4 of the variable are -1.5, 17, -30 and 108. Find the moments about mean,, . Find also the moments about origin, coefficient of skewness and kurtosis.

(b) Obtain the equations of two lines of regression for the following data. Also obtain (i) the estimate of X for Y = 70 (ii) the estimate of Y for X = 71

X   :       65            66        67        67        68        69        70        72

Y   :       67            68        65        68        72        72        69        71                    (8+12)

1. (a) Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boy and 1girl and 3 boys. One child is selected at random from each group. Show that the chance that the three selected consists of 1 girl and 2 boys is 13/32.

(b) (i)  State Baye’s Theorem .

(ii) In a bolt factory machines A, B and C manufacture respectively 25%, 35% and 40% of total. Of their output 5, 4, 2 percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What are the probabilities that it was manufactured by machines A, B and C?                                                    (8+12)

1. (a) Two random variable X and Y have the following joint p.d.f.:

Find (i) Marginal p.d.f. of X and Y.

(ii) Conditional density functions.

(iii) Var(X) and Var(Y).

(iv) Covariance between X and Y.

(b) Find the mean and variance of Binomial distribution.                                   (12+8)

Go To Main Page

## Loyola College B.Sc. Computer Science April 2008 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

# BH 4

THIRD SEMESTER – APRIL 2008

# CS 3204 / 3201/ 4200 – STATISTICAL METHODS

Date : 05/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

# PART A (Answer ALL questions)                                                                       10 ´ 2 = 20

1. Find the simple mean and weighted arithmetic mean of the first ‘n’ natural numbers,

the weights being the corresponding numbers.

1. The first two moments of distribution about the value 4 of the variable are -1.5 & 17. Find μ2.
2. Write any two properties of regression coefficient.
3. Can Y = 5 + 2.8 X & X = 3 – 0.5 Y be the estimated regression equations of Y on X and X on Y respectively.
4. If , then prove that .
5. Two coins are tossed simultaneously. What is the probability of getting (i) a tail (ii) atmost two tails
6. Let X be a random variable with probability distribution.
 X -1 2 3 P(X=x) 1/6 1/2 1/3

Find E(X).

1. Let X be a continous random variable with probability density function given by

Find the constant k.

1. Prove that .
2. Define Binomial distribution.

# PART B (Answer ALL questions)                                                                  5 ´ 8 = 40

1. (a). An incomplete frequency distribution is given as follows:

 Variable Frequency Variable Frequency 10 – 20 12 50 – 60 ? 20 – 30 30 60 – 70 25 30 – 40 ? 70 – 80 18 40 – 50 65 Total 229

Given that the mean value is 46. Determine the missing frequencies using median formula.

(OR)

(b). For a group of 200 candidates the mean and standard deviation of scores were found to be 40 and 15 respectively. Later it was discovered that the scores 43 and 35 were misread as 34 and 53 respectively. Find the correct mean and standard deviation corresponding to the corrected figures.

1. (a). Two sample polls of votes for two candidates A and B for a public office are taken, one from among the residents of rural areas. The results are given in adjoining table. Examine whether the nature of the area is related to voting preference in this election
 Votes for Area A B Total Rural 620 380 1000 Urban 550 450 1000 Total 1170 830 2000

(χ 2 0.05    for 1, 3, 4, 5 d.f are 3.841, 7.815, 9.485, 11.07 respectively).

(OR)

(b). Obtain the equations of two lines of regression for the following data. Also obtain the estimated of X for Y = 70.

X:        65        66        67        67        68        69        70        72

Y:        67        68        65        68        72        72        69        71

1. (a). A and B throw alternatively with a pair of balanced dice. A wins if he throws a sum of six points before B throws a sum of seven points, while B wins if he throws a sum of seven points before A throws a sum of six points. If A begins the game, show that this probability of winning is 30/61.

(OR)

(b) State and prove Baye’s theorem.

1. (a). If X and Y are two random variables having joined density function

Find (i)

(ii)

(iii)

(OR)

(b). A random variable X is distributed at random between the values 0 and 1 so that

its probability density function is , where k is a constant. Find

the value of k, find its mean and variance.

1. (a). (i) Find the mean and variance of Uniform distribution and (5+3)

(ii) If X is Uniform distributed with mean 1 and variance  4/3, then find P (X < 0).

(OR)

(b). Find the moment generating function of the exponential distribution and hence

find its mean and variance.

# PART C (Answer ANY TWO questions)                                                2 ´ 20 = 40

1. (a) A number of particular articles have been classified according to their weights. After drying for 2weeks the same articles have been again been weighted &similarly classified. It is known that the median weight in the first weighing was 20.83 gm, while in the second weighing it was 17.35 gm. Some frequencies a and b in the first weighing and x and y in the second are missing. It is known that a = x/3 and b = y/2. Find the values of the missing frequencies.
 Frequencies for weighing Frequencies for weighing Class I II Class I II 0 – 5 a x 15 – 20 52 50 5 – 10 b y 20 – 25 75 30 10 – 15 11 40 25 – 30 22 28

(b).  A sample analysis of examination results of 200 MBA ‘s was made .It was found that 46 students had failed, 68 secured III division, 62 secured II division , and the rest were placed in I division. Are these figures commensurate with a general examination result which is in the ratio 4:3:2:1 for various categories respectively?

2 0.05    for 3, 4, 5 d.f are 7.815, 9.485, 11.07).                                     (10+10)

1. (a) State and prove addition theorem of probability.

(b) In a bolt factory machines A, B, and C manufacture respectively 25%, 35% and

40% of the total. Of their output 5, 4, 2 percent respectively are defective bolts. A

bolt is drawn at random from the product and is found to be defective. What are

the probabilities that it was manufactured by machines (i) A, (ii) B and (iii) C?

(8+12)

1. (i) Two random variables X and Y have the following joint probability density function:

Find     (a) the constant k.

(b) Marginal density functions of X and Y.

(c) Conditional density functions and (d) Var (X), Var (Y), Cov (X, Y).

(ii) Find the Moment Generating Function of Poisson distribution and hence find the mean and variance.                                                                                 (12+8)

Go To Main Page

## Loyola College B.Sc. Computer Science April 2012 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

THIRD SEMESTER – APRIL 2012

# CS 3204/CA 3201 – STATISTICAL METHODS

Date : 11-11-20112            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART A (Answer ALL the questions)                                                       (10 x 2 = 20)

1. State any two merits of mean.
2. Milk is sold at the rates of 8, 10, 12, 15 rupees per litre in four different months. Assuming that equal amount are spent on milk by a family in the four months find the average price in rupees per month.
3. Define coefficient of variation.
4. The ranks of some 16 students in Mathematics and Physics are as follows: Two numbers within brackets denote the ranks of the students in Mathematics and Physics (1,1) (2,10) (3,3) (4,4) (5,5) (6,7) (7,2) (8,6) (9,8) (10,11) (11,15) (12,9) (13,14) (14,12) (15,16) (16,13). Calculate the rank correlation coefficient for Proficiencies of this group in Mathematics and Physics.
5. If A and B are independent events, then prove that and  are also independent.
6. What is the chance a leap year selected at random will contain 53 Sundays.
7. Let X be a random variable with probability distribution.
 X -1 2 3 P(X=x) 1/6 1/2 1/3

Find E().

1. Let X be a continuous random variable with probability density function given by

Find the constant k.

1. Prove that .
2. Define Binomial distribution.

PART B (Answer ALL the questions)                                                          (5 x 8 = 40)

1. (a) (i) The first two samples have 100 items with mean 15 and standard deviation is 3. If the whole group has 250 items with mean 15.6 and standard deviation is . Find the standard deviation of the second group.

(ii) Find median and mode for the following distribution:

 Class interval 0 -10 10-20 20 -30 30 -40 40- 50 50 -60 60 -70 70 -80 Frequency 5 8 7 12 28 20 10 10

(OR)

(b) Obtain the rank correlation coefficient for the following data:

X:        65        66        67        67        68        69        70        72

Y:        67        68        65        68        72        72        69        71

1. (a) In a partially destroyed laboratory record of an analysis of correlation the following results only are legible. Variance of X = 9 Regression equations:

8 X – 10 Y + 66 = 0.  40 X – 18 Y = 214.What are (i) the mean values of X and Y (ii) The correlation coefficient between X and Y (iii) The standard deviation of Y?

(OR)

(b) Two sample polls of votes for two candidates A and B for a public office are taken, one from among the residents of rural areas. The results are given in adjoining table. Examine whether the nature of the area is related to voting preference in this election

 Votes for Area A B Total Rural 620 380 1000 Urban 550 450 1000 Total 1170 830 2000

(χ 2 0.05    for 1, 3, 4, 5 d.f are 3.841, 7.815, 9.485, 11.07 respectively).

1. (a) A and B throw alternatively with a pair of balanced dice. A wins if he throws a sum of six points before B throws a sum of seven points, while B wins if he throws a sum of seven points before A throws a sum of six points. If A begins the game, show that this probability of winning is 30/61.

(OR)

The probabilities of X, Y and Z becoming managers are  and  respectively.

The probabilities that the Bonus Scheme will be introduced if X, Y and Z becomes managers are  and  respectively. (i) What is the probability that Bonus Scheme will be introduced, and (ii) if the Bonus Scheme has been introduced, what is the probability that the manager appointed was X?

1. (a) A random variable X is distributed at random between the values 0 and 1 so that

its probability density function is , where k is a constant. Find the value of k, find its mean and variance.

(OR)

(b) The joint probability distribution of two random variables X and Y is given by:

and .

Find (i) Marginal distributions of X and Y, and (ii) the conditional probability

distribution of X given Y=1.

1. (a) Find the moment generating function of the Binomial distribution and hence

find its mean and variance.

(OR)

(b) Find the moment generating function of the exponential distribution and hence

find its mean and variance.

PART C (Answer any TWO questions)                                          (2 x 20 = 40)

1. (a) An incomplete frequency distribution is given as follows:

 Variable Frequency Variable Frequency 10 – 20 12 50 – 60 ? 20 – 30 30 60 – 70 25 30 – 40 ? 70 – 80 18 40 – 50 65 Total 229

Given that the median value is 46. Determine the missing frequencies using median

formula.

(b) Calculate (i) Quartile deviation (Q .D) and (ii) Mean Deviation (M.D) from median     for following data:

Marks              :  0-10     10-20     20-30     30-40     40-50     50-60     60-70

No of students:    6            15           8            15           7            6            3.       (10+10)

1. (a) State and prove Baye’s theorem

(b) State and prove the addition theorem of probability.

(12+8)

1. (a) Two random variables X and Y have the following joint probability density

function :

Find (i) Marginal density functions of X and Y.

(ii) Conditional density functions (iii) Var (X), Var (Y) and

(iv) Covariance between X and Y.

(b) If X is a Poisson variate such that P (X = 2) = 9 P (X = 4) + 90 P (X = 6) then

find the mean.

(15+5)

Go To Main Page

© Copyright Entrance India - Engineering and Medical Entrance Exams in India | Website Maintained by Firewall Firm - IT Monteur