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.