IGNOU PGDAST MST 002 Descriptive Statistics Solved Assignment ENGLISH

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MST 002 (January 2026 - July 2026) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-002: Descriptive Statistics

Course Code: MST-002
Assignment Code: MST-002/TMA/2026
Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are true or false and also give the reason in support of your answer: (5×2=10)

(a) If and are the variate values of two variables X and Y, and their geometric means are G₁ and G₂, respectively, then geometric mean of will be (G₁/G₂).

(b) If X and Y are two independent variables and the variables and , then the

(c) If each value of X is divided by 2 and of Y is multiplied by 2, then b'_YX will be same as b.

(d) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.

(e) If and then .

2. (a) The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y + 2), (Y - 3) and (Y + 6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series. 

(b) The following is the distribution of age (in years) of 800 workers:

Age Group	No. of Workers
20 — 25	50
25 — 30	70
30 — 35	100
35 — 40	180
40 — 45	150
45 — 50	120
50 — 55	70
55 — 60	60

Find (i) Median, (ii) Quartile Deviation, and (iii) Coefficient of Quartile Deviation

3. (a) The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs.

(b) Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
and . 

4. (a) The following table shows the information as:

Statistical Measures	Advertisement Expenditure (X) (Rs. Lakhs)	Sales (Y) (Rs Lakhs)
Mean	20	100
Standard Deviation	03	12

 

. Then find

(i) the expected advertising expenditure of the company if sale is Rs. 125 lakhs, and
(ii) the expected sales of the company if the advertising expenditure is Rs 32 lakhs.
(b) Given the following data:
, and then find (i) r_12.3 (ii) r_13.2 (iii) r_23.1 (iv) R_1.23 

5. (a) An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 well to do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well to do; also 587 well to do families were those of farmers and out of them only 156 were having at least one graduate. Obtain all the ultimate class frequencies. 

(b) Can vaccination be regarded as a preventive measure for smallpox from the given data:
(i) Of 1482 persons in a locality exposed to smallpox, 368 in all were attacked, and
(ii) Of 1482 persons, 343 had been vaccinated and of these only 35 were attacked.
 

6. (a) In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as and . The standard deviation of , then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y. 

(b) Suppose X and Y are the two variables having the correlation coefficient 0.85. The following are the values they have:

X	Y
10	40
30	30
50	70
60	80

If two new variables X' and Y' are obtained by adding 50 to each value of X and 100 to each value of Y, respectively, calculate the correlation coefficient between X' and Y' using the above data. Also compare the results.

7. (a) 50% of items have characteristics A and B both, 35% have A, but not B, 25% have B but not A. Show that there must be some misprints in this report.

(b) In the given data, two frequencies are missing and its mean is found to be 1.46.

No. of Accidents (x)	Frequencies (f)
0	46
1	?
2	?
3	25
4	10
5	5
Total	200

Find the missing frequencies

 

 

MST 002 2025 - English

TUTOR MARKED ASSIGNMENT

MST-002: Descriptive Statistics

Course Code: MST-002

Assignment Code: MST-002/TMA/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1. State whether the following statements are true or false and also give the reason in support of your answer:

(a) if  are the variate values  of two variables X and and their geometric means are Grand G₂, respectively, then geometric mean of  will be (G₁/G₂).

(b) If X and Y are two independent variables and the variables U=X+ Y and V= X-Y, then the

(c) If each value of X is divided by 2 and of Y is multiplied by 2, then b'yx will be same as byx.

(d) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.

(e) If

2.(a) The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y+2), (Y-3) and (Y+6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series.

(b) The following is the distribution of age (in years) of 800 workers:

Age Group	No. of Workers
20 — 25	50
25 — 30	70
30 — 35	100
35 — 40	180
40 — 45	150
45 — 50	120
50 — 55	70
55 — 60	60

Find (i) Median, (ii) Quartile Deviation, and (iii) Coefficient of Quartile Deviation.

3. (a)The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs.

(b) Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:

and

4.(a) The following table shows the information as:

Statistical Measures	Advertisement Expenditure (X) (Rs. Lakhs)	Sales (Y) (Rs Lakhs)
Mean	20	100
Standard Deviation	03	12

(i) the expected advertising expenditure of the company if sale is Rs. 125 lakhs, and

(ii) the expected sales of the company if the advertising expenditure is Rs 32 lakhs.

b) Given the following data: 

 (i) r_12.3 (ii) r_13.2(iii) r _23.1 (iv) R_1.23

5. (a) An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 well to do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well to do; also 587 well to do families were those of farmers and out of them only 156 were having at least one graduate. Obtain all the ultimate class frequencies.

(b) Can vaccination be regarded as a preventive measure for smallpox from the given data:

(i) Of 1482 persons in a locality exposed to smallpox, 368 in all were attacked, and

(ii) Of 1482 persons, 343 had been vaccinated and of these only 35 were attacked.

6.(a) In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as 8X - 10Y + 70 = 0 and 20X - 9Y - 65 = 0. The standard deviation of X = 3, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y.

(b) Suppose X and Y are the two variables having the correlation coefficient 0.85. The following are the values they have:

X	Y
10	40
30	30
50	70
60	80

If two new variables X' and Y' are obtained by adding 50 to each value of X and 100 to each value of Y, respectively, calculate the correlation coefficient between X' and Y' using the above data. Also compare the results.

7.(a) 50% of items have characteristics A and B both, 35% have A, but not B, 25% have B but not A. Show that there must be some misprints in this report.

(b) In the given data, two frequencies are missing and its mean is found to be 1.46.

No. of Accidents (x)	Frequencies (f)
0	46
1	?
2	?
3	25
4	10
5	5
Total	200

Find the missing frequencies.

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