Loyola College Statistical Methods Question Papers Download
Loyola College B.Sc. Statistics Nov 2003 Statistical Methods Question Paper PDF Download
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)
 Give the definition of statistics according to Croxton and Cowden.
 Comment on the following: “ Sample surreys are more advantageous than census”.
 Give an example for
(i) Quantitative continuous data (ii) Discrete time series data
 Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
 Mention any two limitations of geometric mean.
 From the following results obtained from a group of observations, find the standard deviation. S(X5) = 8 ; S(X5)^{2 }= 40; N = 20.
 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.
 Given below are the lines of regression of two series X an Y.
5X6Y + 90 = 0
15X 8Y130 = 0
Find the values of .
 Write the normal equations for fitting a second degree parabola.
 Find the remaining class frequencies, given (AB) = 400;
(A) = 800; N=2500; (B) = 1600.
SECTION – B
Answer any FIVE questions. (5 ´8 = 40 Marks)
 Explain any four methods of collecting primary data.
 Draw a histogram and frequency polygon for the following data.
Variable  Frequency  Variable  Frequency 
100110  11  140150  33 
110120  28  150160  20 
120130  36  160170  8 
130140  49 
Also determine the value of mode from the histogram.
 Calculate arithmetic mean, median and mode from the following
frequency distribution.
Variable  Frequency  variable  Frequency 
1013  8  2528  54 
1316  15  2831  36 
1619  27  3134  18 
1922  51  3437  9 
2225  75  3740  7 
 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 
 Calculate Bowley’s coefficient of skewness from the following data.
Variable  frequency 
010  12 
1020  16 
20 30  26 
30 40  38 
40 50  22 
5060  15 
60 70  7 
70 80  4 
 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 
 Explain the concept of regression with an example.
 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)
 a) Explain (i) Judgement sampling (ii) Quota sampling and
(iii) Systematic sampling methods with examples.
 (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)
 a) (i) An incomplete distribution is given below
Variable  010  1020  2030  3040  4050  5060  6070 
Frequency  10  20  f_{1}  40  f_{2}  25  15 
Given the median value is 35 and the total frequency is 170, find
the missing frequencies f_{1} 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 
 b) Explain any two measures of dispersion. (7+7+6)
 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.
 Calculate the first four central moments and coefficient of skewness from the
following distribution.
Variable  frequency  Variable  Frequency 
2530  2  4550  25 
3035  8  5055  16 
3540  18  5560  7 
4045  27  6065  2 
(10+10)
 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 
 b) (i) Explain the concept of Kurtosis.
(ii) In a coeducational 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)
Loyola College B.Sc. Statistics April 2004 Statistical Methods Question Paper PDF Download
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)
 Give an example for primary and secondary data.
 What is meant by judgement sampling?
 Mention the difference between histogram and bar diagram?
 What are the characteristics of a good measure of central tendency?
 For a frequency distribution, the mean and mode were found to be 15 and 24 respectively. Find the median of the distribution.
 Comment on the following: “The mean deviation of a frequency distribution about an origin is minimum, when the origin is the mean”.
 Define: Skewness
 Give an example for positive correlation.
 Find the regression equation of y on x given the following information:
 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)
 Explain the different types of classification with examples.
 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.
 Calculate Q_{1}, Q_{2}, P_{3} and P_{20 }from the following data:
Class Interval: 05 510 1015 1520 2025
Frequency : 7 18 25 30 20
 Calculate mean deviation about median and its coefficient from the following data:
Class  Frequency  Class  Frequency 
010  5  4050  20 
1020  8  5060  14 
2030  12  6070  12 
3040  15  7080  6 
 Explain the concepts of correlation and regression through an example.
 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.
 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.
 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)
 i) Explain the various method of collecting primary data.
 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 
1020  6  6070  16 
2030  8  7080  8 
3040  12  8090  5 
4050  18  90100  2 
5060  25 
Also find the value of the median. (10+10)
 i) Calculate mode ( by grouping method) from the following data:
Class interva l: 1020 2030 3040 4050 5060 6070 7080 8090
Frequency : 5 9 13 21 20 15 8 3
 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)
 i) Explain the concept of kurtosis.
 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)
 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.
 ii) Explain any two methods of studying the association between attributes. (15+5)
Loyola College B.Sc. Statistics Nov 2006 Statistical Methods Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – NOV 2006
ST 1500 – STATISTICAL METHODS
(Also equivalent to STA 500)
Date & Time : 01112006/1.004.00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
 Define Statistics.
 Distinguish between primary and secondary data.
 What are the advantages of diagrammatic and graphic presentation of data?
 What are the desirable properties of a good average?
 What purpose does a measure of dispersion serve?
 Interpret r when r = 1, 1, 0, where r is the correlation coefficient.
 What is the purpose of regression analysis?
 Define kurtosis.
 How would you distinguish between association and correlation?
 Check for consistency: (A) = 100, (B) = 150, (AB) = 60, N = 500.
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
 Explain the various methods that are used in the collection of primary data, pointing out their merits and demerits.
 Represent the above frequency distribution by means of a histogram and superimpose the corresponding frequency polygon. Experience (in months).
Experience  02  24  46  68  810  1012  1214  1416 
No. of Workers  5  6  15  10  5  4  2  2 
 (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?
 Calculate Quartile deviation and coefficient of Quartile deviation from the following data:
Wages (in Rs.)  Less than 35  3537  3840  4143  Over 43 
No. of wage earners  14  62  99  18  7 
 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 
 Fit a straight line to the following data.
X  6  2  10  4  8 
Y  9  11  5  8  7 
 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.
 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)
 (i) Define sampling and explain the different methods of sampling.
(ii) Draw an ogive for the following distribution and calculate the median wage.
Wages  10001100  11001200  12001300  13001400  14001500  15001600 
Workers  6  10  22  16  14  12 
 (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” 
 (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.
 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.
Loyola College B.Sc. Statistics April 2007 Statistical Methods Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2007
ST 1500 – STATISTICAL METHODS
Date & Time: 24/04/2007 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
PARTA
Answer all the questions: 10×2=20
 Define statistics.
 Explain ordinal data,nominal data.
 State any two merits of median.
 Find the values of Q_{1} and Q_{3} for the following data.
20,28,40,12,30,15,50
 Write the formulas for β_{1} and β_{2} in terms of the moments.
 Mention the properties of the correlation coefficient.
 Given the two regression equations
8X – 10Y= – 66
40X – 18Y = 214
find the mean values of X and Y.
 What are the normal equations for fitting
Y= ab^{x}?
 Find whether the given data
(A)=100, (B)=150, (AB)=60,N=500 is consistent.
 Explain scatter diagram.
PARTB
Answer any 5 questions: 5×8=40
 Draw the Boxwhisker 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
 Obtain the mean deviation about median for the marks give below;
Marks Frequency
 7
 12
2030 18
3040 25
4050 16
5060 14
6070 8
 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
 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
 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.
 Find the geometric mean for the following data given below.
Marks Frequency
 6
 10
 18
 30
 15
 12
 10
 6
 2
 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.
 Explain the various types of diagrams used in statistical applications.
PARTC
Answer any two questions: 10×2=20
 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
 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.
 Two brands of tyres are tested with the following results.
No of tyres
Life(000 miles) X Y
2025 1 0
2530 22 24
3035 64 76
3540 10 0
4045 3 0
i)Which brand of tyres has greater average life? (5)
ii)Calculate coefficient of variations and state which one is consistent. (15)
 Find β_{1} and β_{2} for the following data and interpret the results.
Age Frequency
 2
 8
 18
 27
 25
 16
 7
 2
 a)Explain the contingency tables and the method of calculating chisquare 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.
Loyola College B.Sc. Statistics April 2008 Statistical Methods Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

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.
 Distinguish between Census and sample.
 State the objectives of classification of data.
 Why do we call Arithmetic mean is a good average?
 When do you say a distribution is skewed? Sketch positive and negative skew ness.
 What is curve fitting?
 Write down the normal equations for fitting .
 If for two variable X and Y, correlation coefficient
find the regression co efficient of X onY.
 If two regression lines are and for two variables X and Y, find the mean values of X and Y.
 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?
 State any two characteristics of Yule’s coefficient of Association.
PART – B
(5 x 8 = 40 marks)
Answer any 5 questions.
 Draw ogive curves for the data given below:
Draw Sales
(Rs.000) 
1020  2030  3040  4050  5060  6070  7080 
No. of Shops  3  6  10  15  8  4  2 
 Distinguish between Classification and Tabulation.
 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 
 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 
 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 
 What do you understand by regression? Why there are two regression equations? What are its uses?
 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 
 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.
 a) Calculate mean deviation from median from the following data.
Class Interval:  2025  2530  3040  4045  4550  5055 
Frequency:  6  12  17  30  10  10 
Class Interval:  5560  6070  7080 
Frequency:  8  5  2 
 b) From the prices of shares X and Y given below, state which share is more stable in value
 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.
 Calculate and from the data given below
Marks:  010  1020  2030  3040  4050  5060  6070 
No. of Students:  8  12  20  30  15  10  5 
 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.
Loyola College B.Sc. Statistics Nov 2008 Statistical Methods Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – November 2008
ST 1500 – STATISTICAL METHODS
Date : 101108 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A (10×2=20)
Answer ALL the questions
 What is a census survey?
 Identify the scale used for each of the following variables
 Calories consumed during the day.
 Marital status.
 Perceived health status reported as poor, fair, good or excellent.
 Blood type
 Mention any four measures of dispersion.
 Give a measure of kurtosis.
 State the principle of least squares.
 What is the standard form of growth curves?
 When will the regression lines be perpendicular to each other?
 If the regression coefficients are b_{XY} = – 0.4 and b_{YX} = – 0.9 find the
correlation coefficient between X and Y.
 What is a dichotomous classification?
 State the relation between Yule’s coefficient of association and
coefficient of colligation.
PART – B (5×8=40)
Answer any FIVE questions
 Describe any two methods of collecting primary data along with their
merits and demerits.
 Explain the importance of diagrammatic representation of data.
 Compute mean and median for the following frequency distribution
Sales target : 1020 2030 3040 4050 5060
(Rs.lakhs)
No. of times
achieved : 6 8 12 9 5
 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?
 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.
 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.
 ii) Mean values of X and Y.
iii) Ratio of the coefficient of variability of X to that of Y.
 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.
 In a certain investigation carried on with regard to 500 graduates and 1500 nongraduates, it was found that the number of employed graduates was 450 while the number of unemployed nongraduates was 300.
In the second investigation 5000 cases were examined. The number of
nongraduates was 3000 and the number of employed nongraduates was
 The number of graduates who were found to be employed was
 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
 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 : 300310 310320 320330 330340 340350
No. of workers : 9 20 24 38 48
Output in units : 350360 360370 370380
No. of workers : 27 17 7
 Calculate a measure of dispersion and a measure of skewness based on quartiles from the following distribution:
Wages (Rs.): below 35 3537 3840 4143 over 43
No.of wage
earners : 14 60 95 24 7
 Consider the following data where x is temperature (in ^{o}c) 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.
 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 7milligram dose of this poison.
Loyola College B.Sc. Statistics April 2009 Statistical Methods Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

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
 States any two applications of statistics.
 Distinguish between primary and secondary data.
 What are the characteristics of a good measure of central tendency?
 Find the coefficient of variation from the following data.
.
 State the principle of least squares.
 Write the normal equations for fitting the curve .
 The ranks of two attributes in a sample are given below. Find the correlation between them.
 If and are the regression coefficients of y on x and x on y respectively, show that.
 Check whether A and B are independent given the data:
N=10,000, (A)=4500, (B)=6000, (AB)=3150
 Distinguish between correlation and regression.
PART – B
Answer any FIVE questions: 5 x 8 = 40
 Explain classification and tabulation of data.
 Draw less than and more than ogives from following data:
Profits:
(Rs. Lakhs 
1020  2030  3040  4050  5060 
No. of
Companies: 
6  8  12  18  25 
Profits:
(Rs. Lakhs) 
6070  7080  8090  90100  
No. of companies: 
16  8  5  2 
 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 
 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.
 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 
 Show that the coeffient of correlation lies between 1 and +1.
 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.
 Given the following data, find the two regression equations:
PART – C
Answer any TWO questions: 2 x 20 = 40
 a) Explain the scope and limitations of statistics.
 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 
200250  4  4  2  1  11 
250300  3  5  4  2  14 
300350  2  6  8  5  21 
350400  1  4  6  10  21 
10  19  20  18  67 
 a) Define measure of dispersion. Prove that the standard deviation is independent of change of origin but not scale.
 b) Find the coefficient of quartile deviation from the following data.
Wages:  010  1020  2030  3040  4050  
No.of
Workers: 
22  38  46  35  20 
 Calculate the first four moments about the mean and also the values of and from the following data:
Marks:  010  1020  2030  3040  4050  5060  6070  
No. of Students:  8  12  20  30  15  10  5 
 a) Fit the curve using the principle of least squares.
 b) From the following data, calculate the remaining frequencies and hence test whether A and B are
independent.
.
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 : 101110 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL the questions [10×2=20]
 State any two limitations of statistics.
 Write down the types of Scaling with examples.
 Define measures of central tendency.
 What do you mean by skewness?
 Write down the normal equations for the exponential curve.
 What is curve fitting?
 State the assumptions underlying in Karlpearson’s correlation coefficient.
 Define probable error.
 Examine the consistency of the following data:
N= 1000; (A)= 600; (B)= 500; (AB)= 50.
 Write the Yule’s Coefficient of association between the attributes.
PART – B
Answer any FIVE questions [5×8=40]
 Describe the various types of diagrammatic representation of data.
 Draw the cumulative frequency curve. find the quartiles for the following data:
Marks  010  1020  2030  3040  4050  5060  6070 
No of Students  4  8  11  15  12  6  3 
 Find the missing frequencies using the median value 46 for the following data:
Variable  1020  2030  3040  4050  5060  6070  7080  Total 
Frequency  12  30  ?  65  ?  25  18  219 
 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.
 Show that the correlation coefficient cannot exceed unity.
 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 
 Find the association of A and B in the following cases:
 N = 1000; (A)= 470; ( B)= 620 and (AB)= 320
 (A)= 490; (AB)= 294; (α)= 570 and (αβ)= 380
 (AB)= 256; (αB)= 768; ( Aβ)= 48 and ( αβ)= 144.
 Find the angle between the two regression lines.
PART – C
Answer any TWO questions [2×20=40]
 a) Describe the various types of classification and tabulation of data in detail. (12)
 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)
 a) For a distribution, the mean is 10, variance is 16, γ_{1} is +1 and β_{2} is 4. Obtain
the first four moments about the origin. Make a comment on distribution.
 b) Calculate i) Quartile Deviation and ii) Mean Deviation from mean for the
following data:
Marks  010  1020  2030  3040  4050  5060  6070 
No of Students  6  5  8  15  7  6  3 
 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  
1020  4  2  2  0  8 
2030  5  4  6  4  19 
3040  6  8  10  11  35 
4050  4  4  6  8  22 
5060  0  2  4  4  10 
6070  0  2  3  1  6 
Total  19  22  31  28  100 
 b) Predict the value of Y when X=6 for the following data:
Σx=55; Σxy=350; Σy=55; Σx^{2}=385 and n=10.
 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 
 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.
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 : 19042011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART – A
Answer ALL questions 10×2=20
 Write any two limitation of statistics.
 What is classification?
 Mention Various measures of central tendency.
 Define Skewness.
 Write the normal equations to fit a parabola by the principles of least squares.
 Explain curve fitting.
 Define correlation.
 State any two properties of regression coefficients.
 Find the missing frequencies from the following data, (A)=400, (AB)=250, (B)=500, N=1200.
 Explain Yule’s coefficient of association.
PART – B
Answer any FIVE questions. 5×8=40
 Explain the various types of classification of data.
 Distinguish between primary data and secondary data.
 Find Arithmetic mean and mode for the following data:
Profit per shop: 010 1020 2030 3040 4050 5060
No. of shops : 12 18 27 20 17 6
 Define Kurtosis. Also explain various measures of Kurtosis.
 Fit a straight line trend for the following data:
Year: 1994 1995 1996 1997 1998 1999
Production 7 9 12 15 18 23
 What is a scatter diagram? How does it help us in studying the correlation between two variables with respect to their nature of relationship?
 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
 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
 a) What do you understand by Tabulation? What are the different parts of a table?
Explain. (2+8)
 b) Draw a histogram and frequency polygon to represent the following data.
Weekly wages: 1015 1520 2025 2530 3035 3540
No. of workers; 7 19 27 15 12 8 (7+3)
 a) Calculate mean deviation from mean for the following data:
Class interval: 24 46 68 810
No. of person: 3 4 2 1 (3+5)
 b) Calculate Bowley’s coefficient of Skewness from the following data:
Marks: 110 1020 2030 3040 4050 5060 6070 7080
No. of
persons: 10 25 20 15 10 35 25 10 (12)
 a) Write the procedure to fit a second degree parabola using method of least squares.
(6)
 b) Fit a second degree parabola to the following.
Year ; 1978 1979 1980 1981 1982 1983
Price: 100 107 128 140 181 192 (14)
 a) Show that the coefficient of correlation lies between 1 and +1. (10)
 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)
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 : 28042012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL questions: (10 x 2 = 20 marks)
 State any two limitations of statistics.
 What is meant by classification?
 Define dispersion.
 Explain Kurtosis.
 What is curve fitting?
 Explain the principle of least squares.
 Define correlation with an example.
 State any two properties of regression coefficients.
 Explain association of attributes.
 Define Independence of attributes.
PART – B
Answer any FIVE questions: (5 x 8 = 40 marks)
 Explain the Scope of statistics.
 Describe Nominal and Ordinal scaling. Also write their advantages.
 Define skewness. Explain the various measures of skewness.
 Calculate the mean and mode for the following frequency distribution:
Monthly Wages: Less than 200 200400 400600 600800 800100
No. of workers: 78 165 93 42 12
 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
 Prove that the coefficient of correlation lies between 1 and +
 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
 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
 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)
 a) Explain the applications of diagrams and graphs and state their advantages.
 b) Define Primary data. What are the sources of primary data?
 Calculate first four moments about mean from the following data. Also calculate b_{1} and
b_{2} 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
 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)
 b) Calculate KarlPearson’s coefficient of correlation from the following data.
X: 10 12 18 24 23 27
Y: 13 18 12 25 30 10 (8 marks)
 a) Given the following data, find the two regression equations:
(8 marks)
 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)
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)
 Why is sampling necessary under certain conditions?
 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?
 List the requisites of a good measure of central tendency.
 What is meant by Kurtosis?
 State the principles of least squares.
 What is the general form of growth curves?
 Define rank correlation coefficient.
 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
 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?
 What is meant by coefficient of colligation?
PART – B
Answer any FIVE questions: (5 x 8 = 40 marks)
 The survey about colour preferences reported the age distribution of the people who responded.
Age group (years)  118  1924  2535  3650  5169  7074 
count  10  97  70  36  14  5 
Draw ‘less than ogive’ curve and locate the median.
 Describe the various ways of classification of statistical data with suitable illustrations.
 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.
 Describe the construction of Lorenz curve.
 What is skewness? Distinguish diagrammatically the different types of skewness.
 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 
 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 
 Describe the conditions for consistency of data when there are three attributes.
PART – C
Answer any TWO questions (2 x 20 = 40 marks)
 (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)
 (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
daycare center:
Weight (in pounds)  1019  2029  3039  4049  5059  6069  7079 
No. of children  5  19  10  13  4  4  2 
Calculate mean deviation about median. (10 marks)
 (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)
 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.
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

THIRD SEMESTER – NOV 2006
CS 3201 – STATISTICAL METHODS
Date & Time : 31102006/9.0012.00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL the questions. 10 × 2 = 20
 Define Geometric Mean.
 Find the mode for the following distribution:
Class interval: 010 1020 2030 3040 4050 5060 6070
Frequency : 5 8 7 12 28 20 10
 State the properties of regression lines.
 Write the application of chisquare test.
 Three coins are tossed. What is the probability of getting at least one head?
 What is the chance that a leap year selected at random will contain 53 Sundays?
 Find the expectation of the number on a die when thrown.
 If X and Y are two random variables, determine whether X and Y are independent for the following joint probability density function
.
 Find the moment generating function of Uniform distribution.
 Write the probability density function of Normal distribution.
SECTION B
Answer ALL the questions. 5 × 8 = 40
 (a) Calculate the mean and median for the following frequency distribution.
Class interval: 08 816 1624 2432 3240 4048
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 : 010 1020 2030 3040 4050 5060 6070
No of students : 6 5 8 15 7 6 3
 (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.
 (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 classgroup. Test the hypothesis at 5% level that opinions are independent of the class groupings. (Given value of chisquare 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 
 (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  .27  0 
0  .08  .04 
2  .16  .10 
3  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.
 (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
 (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)
 (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)
 (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)
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

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
 Find the simple mean and weighted arithmetic mean of the first ‘n’ natural numbers,
the weights being the corresponding numbers.
 The first two moments of distribution about the value 4 of the variable are 1.5 & 17. Find μ_{2}.
 Write any two properties of regression coefficient.
 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.
 If , then prove that .
 Two coins are tossed simultaneously. What is the probability of getting (i) a tail (ii) atmost two tails
 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).
 Let X be a continous random variable with probability density function given by
Find the constant k.
 Prove that .
 Define Binomial distribution.
PART B (Answer ALL questions) 5 ´ 8 = 40
 (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.
 (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
 (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.
 (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.
 (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
 (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?
(χ^{2} _{0.05 }for 3, 4, 5 d.f are 7.815, 9.485, 11.07). (10+10)
 (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)
 (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)
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 : 111120112 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART A (Answer ALL the questions) (10 x 2 = 20)
 State any two merits of mean.
 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.
 Define coefficient of variation.
 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.
 If A and B are independent events, then prove that and are also independent.
 What is the chance a leap year selected at random will contain 53 Sundays.
 Let X be a random variable with probability distribution.
X  1  2  3 
P(X=x)  1/6  1/2  1/3 
Find E().
 Let X be a continuous random variable with probability density function given by
Find the constant k.
 Prove that .
 Define Binomial distribution.
PART B (Answer ALL the questions) (5 x 8 = 40)
 (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  1020  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
 (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).
 (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?
 (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.
 (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)
 (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 : 010 1020 2030 3040 4050 5060 6070
No of students: 6 15 8 15 7 6 3. (10+10)
 (a) State and prove Baye’s theorem
(b) State and prove the addition theorem of probability.
(12+8)
 (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)