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

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 AC 01

FIRST SEMESTER – APRIL 2007

# ST 1500 – STATISTICAL METHODS

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

# PART-A

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

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

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

8X – 10Y= – 66

40X – 18Y = 214

find the mean values of X and Y.

1. What are the normal equations for fitting

Y= abx?

1. Find whether the given data

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

1. Explain scatter diagram.

PART-B

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

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

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

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

Marks                                           Frequency

• 7
• 12

20-30                                                    18

30-40                                                    25

40-50                                                    16

50-60                                                    14

60-70                                                     8

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

X   75    88    95    70    60     80    81     50

Y  120  134  150  115  110   140  142   100

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

Year    1997    1998    1999    2000    2001    2002    2003

Production     42         49        62        75        92      122      158

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

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

and failure are independent.

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

Marks                        Frequency

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

girls.The results were as follows.

Boys                   Girls

Mean              72                       73

SD                7                       6.4

Sample size      150                     250

Find the combined mean and combined standard deviation.

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

### PART-C

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

workers selected at random.

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

Productivity

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

i)Obtain the regression equation of Y on X

ii)Obtain the regression equation of X on Y

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

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

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

equations.

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

No    of    tyres

Life(000 miles)                                        X        Y

20-25                                                 1          0

25-30                                                22        24

30-35                                                64        76

35-40                                                10         0

40-45                                                 3          0

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

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

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

Age                                    Frequency

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

contingency table.

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

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

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

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

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