LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600  034

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

 

4. Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
5. Mention any two limitations of geometric mean.
6. 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.

 

7. 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.

 

8. 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 .

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

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

                                                 SECTION – B

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

11. Explain any four methods of collecting primary data.
12. 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.

 

 

 

 

 

 

13. 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

 

14. 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

 

15. 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

 

16. 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

 

17. Explain the concept of regression with an example.
18. 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 = ab^X  for the above data and estimate the

sales for the year 1997.

 

 

 

 

 

SECTION – C

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

 

19. 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)

 

20. 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 f_2.

• 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)

22. 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)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2004

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)

 

11. Explain the different types of classification with examples.

 

12. 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.

 

13. 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

 

 

 

14. 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

 

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

 

16. 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.

 

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

Total Adults:               10,000

Literate:                         1,290

Unemployed:                1,390

Literate unemployed:       820

Comments on the results.

 

18. 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)

 

19. i) Explain the various method of collecting primary data.
20. 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)

 

 

 

 

 

20. 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)

21. 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)

 

22. 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)

 

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                          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.

 

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                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

Answer all the questions:                                       10×2=20

 

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

5. Write the formulas for β₁ and β₂ in terms of the moments.
6. Mention the properties of the correlation coefficient.
7. 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= ab^x?

1. Find whether the given data

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

10. Explain scatter diagram.

 

PART-B

Answer any 5 questions:                                                                                   5×8=40

 

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

13. 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

14. 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

15. 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.

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

Marks                        Frequency

• 6
• 10
• 18
• 30
• 15
• 12
• 10
• 6
• 2

17. 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.

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

 

PART-C

Answer any two questions:                                                                            10×2=20

 

19. 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.

 

20. 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)

 

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

Age                                    Frequency

• 2
• 8
• 18
• 27
• 25
• 16
• 7
• 2

22. 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.

 

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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)

Answer ALL the questions.

 

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)                 

Answer any 5 questions.      

 

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)

Answer any TWO questions.

 

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.

 

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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)

Answer ALL the questions

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 b_­XY­ = – 0.4 and b_­YX­ = – 0.9 find the

correlation coefficient between X and Y.

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

coefficient of colligation.

 

PART – B                                 (5×8=40)

Answer any FIVE questions

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

merits and demerits.

12. Explain the importance of diagrammatic representation of data.
13. 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

14. 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, ∑X_­­² = 902.8, ∑Y = 261, ∑_­Y_­² = 1457.6

Which is more varying, the length or weight?

15. 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.

 

 

 

16. 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.

17. 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.

18. 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

non-graduates was 3000 and the number of employed non-graduates was

2500. The number of graduates who were found to be employed was
2501. 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)

Answer any TWO questions

 

19. 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

20. 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

21. Consider the following data where x is temperature (in ^oc) and Y is the number of eggs per cm_­² .

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.

22. 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.

 

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     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.

.

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

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

10. Distinguish between correlation and regression.

PART – B

Answer any FIVE questions:                                                               5 x 8 = 40

 

11. Explain classification and tabulation of data.
12. 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

13. 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

14. 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.
15. 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

16. Show that the coeffient of correlation lies between -1 and +1.
17. 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.
18. Given the following data, find the two regression equations:

PART – C

Answer any TWO questions:                                                               2 x 20 = 40

19. a) Explain the scope and limitations of statistics.
20. 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

20. a) Define measure of dispersion. Prove that the standard deviation is independent of change of origin but not scale.
21. 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

21. 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

22. a) Fit the curve using the principle of least squares.
23. b) From the following data, calculate the remaining frequencies and hence test whether A and B are

independent.

.

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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

 Answer ALL the questions                                                                                                             [10×2=20]

 

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

 

 Answer any FIVE questions                                                                                                           [5×8=40]

 

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

17. 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.

18. Find the angle between the two regression lines.

 

PART – C

Answer any TWO questions                                                                                                       [2×20=40]

 

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=ab^x to the following data:

X	1	2	3	4	5	6	7	8
Y	1.0	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.

 

 

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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

Answer ALL questions                                                                                           10×2=20

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

Answer any FIVE questions.                                                                                 5×8=40

11. Explain the various types of classification of data.
12. Distinguish between primary data and secondary data.
13. 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

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

Year:             1994         1995           1996               1997               1998               1999

Production      7             9                12                 15                  18                  23

16. What is a scatter diagram? How does it help us in studying the correlation between two variables with respect to their nature of relationship?
17. 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

 

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

Passed                       Failed             Total

Married                         90                                 65                 155

Unmarried                   260                             110               370

 

PART – C

Answer any TWO questions                                                                                  2×20=40

 

19. 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)

20. 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)

 

21. 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)

 

22. 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)

 

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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)

 

11. Explain the Scope of statistics.
12. Describe Nominal and Ordinal scaling. Also write their advantages.
13. Define skewness. Explain the various measures of skewness.
14. 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

15. 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

16. Prove that the coefficient of correlation lies between -1 and +
17. 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

18. 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)

 

19. 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

21. 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)

22. 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)

 

 

 

 

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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 = ab^t 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	3.0	3.4	4.2	8.1	9.7	16.3

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

 

 

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