No. of Printed Pages: 7 IMST-0021
POST GRADUATE DIPLOMA IN APPLIED STATISTICS (PGDAST) Term-End Examination 001..07 June, 2016
MST-002 DESCRIPTIVE STATISTICS
Time hours Maximum Marks: 50
Note: Question no. 1 is compulsory. Questions no. 2 to 5
have internal choices. Use of scientific calculator is allowed.
(iii) Use of Formulae and Statistical Tables Booklet for
PGDAST is allowed. Symbols have their usual meaning.

1. State whether the following statements are true or false. Give reasons in support of your answers. The weighted mean of n natural numbers is (2n if weights are the corresponding numbers. The values of regression coefficients byx and bxy are 1/5 and 10 respectively. If Y is proportional to then =1. In case of consistent data, no class frequency can be negative. If 25 is subtracted from each value of X and Y and then divided by 10, the new byx is 2 1/2 times of byx.

2. The annual rates of growth of output of a factory in 5 years are 5.0, 7.5, 2.5, 5.0 and 10.0, respectively. What is the compound rate of growth of output per annum for the period? 4

The number of employees, average daily wages and the variance of the wages for two factories are given as

Factory A Factory B
Number of employees 50 100
Average daily wage 120 85
Variance of daily wages 09 16 In which factory is there a greater variation in the distribution of daily wages?

(ii) Suppose in factory the daily wages of an employee were wrongly noted as Rs 120 instead of Rs 100. What would the correct variance for factory B be

OR

The data of monthly profit (in lacs) of various companies is given as follows:

Monthly Profit (in lacs) Number of Companies
Less than 7.5 04
7.5 -12.5 10
12.5-17.5 20
17.5-22.5 36
22.5-27.5 16
27.5-32.5 12
32.5-37.5 02

Determine whether the distribution is symmetric and mesokurtic by calculating the moments, B1 and B2

3. A computer while calculating the correlation coefficient between the variables X and Y obtained the following results:

N 30, EX 120, EY 90, EX^2 600, Ey^2 EXY =335

It was, however, later discovered at the time of checking that it had copied wrongly, two pairs of observations as 10) and while the correct values were 12) and respectively. Obtain the correct value of the correlation coefficient
between X and Y.

The coefficient of rank correlation of the marks obtained by 10 students in Statistics and Accountancy was found to be 0.8. It was later discovered that the difference in ranks in the two subjects obtained by one of the students was taken as 7 instead of 9. Find the correct value of the rank correlation coefficient.

OR In order to find the correlation coefficient between X and Y from 12 pairs of observations, the following calculations were made:

EX 30, EY EX^2 670, Ey^2 285, EXV 334

On subsequent verification it was found that the pair was copied wrongly while the correct value was Y Find the correct value of the correlation coefficient. 7 An examination of eight applicants for a clerical post was taken by a firm. From the marks obtained by the applicants in the Accountancy and Statistics papers, compute the rank correlation coefficient to check how far the competence of the applicants in both subjects go together?

Applicant: A B C D E F G H
Marks in Accountancy 15 20 28 12 40 60 20 80
Marks in Statistics 40 30 50 30 20 10 30 60

4. The regression equation of Y on X and X on Y are Y 2X and 6X respectively and the second moment of X about the origin is 3. Find the mean values of X and the value of the correlation coefficient, and the standard deviation of Y

Suppose a data analyst has found r12=0.96, rl3 =0.36 and r23 0.78 for a given set of values of X1, X2 and X3. Examine whether their computations may be said to be free from error.

OR

Given the following bivariate data.

X: 5 3 2 1 1 7 3
Y: 1 0 0 1 2 1 5 Fit a regression line of Y on X and find if X =10.

(ii) Fit a regression line of X on Y and find if Y 2.5.

5. The following ultimate class frequencies are given as:
(ABC) 60, 250, 80, 55 and =8200.
Find the frequencies of all positive classes. What is meant by a class frequency of first order, and third order? How would you express a class frequency of first order in terms of class frequencies of third order?

OR

A company is interested in determining the strength of association between the communicating time of their employees and the level of stress-related problems observed on job. A study of 116 assembly workers reveals the following:

Communicating Stress Total
Time High Moderate Low
Under 20 minutes 9 5 18 32
20 -50 minutes 17 8 28 53
Over 50 minutes 18 6 7 31
Total 44 19 53 116

Use the coefficient of contingency to determine the amount of association between the communicating time and stress, given Cmax =0.816.