MST-002 Solved Assignment 2021
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MST-002 Solved Assignment 2021
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MST-002 Solved Assignment 2021
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MST-002 Solved Assignment 2021
MST-002 Assignment Question Paper
(Descriptive Statistics)
MST-002: Descriptive Statistics
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:
- If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
- Mean deviation is least when calculated from the median.
- The correlation coefficient between x and (a – x) is –1.
- The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
- If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.
2. a) Compute the coefficient of variation for factory A and B from the following:
|
Daily Wages (Rs.) : |
12 |
15 |
17 |
22 |
25 |
30 |
|
Workers in Factory A: |
5 |
10 |
20 |
35 |
12 |
8 |
|
Workers in Factory B: |
15 |
25 |
30 |
35 |
21 |
19 |
Find: (i) Which factory pays higher average daily wages?
(ii) In which factory are wages more variable?
b) The mean and the standard deviation of a characteristic of 100 items were found to be 60 and 10 respectively. At the time of calculations, two items were wrongly taken as 5 and 45 instead of 30 and 20. Calculate the correct mean and corrected standard deviation.
3.Calculate the first four moments of the following distribution about the mean and hence find β1 and β2.
|
X: |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
F: |
1 |
8 |
28 |
56 |
70 |
56 |
28 |
8 |
1 |
4(a) Fit an exponential curve of the from Y = abX 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) In a partially destroyed laboratory, record of an analysis of correlation data, the following results only are legible:
Variance of X = 9. Regression equations: 8X – 10Y + 66 = 0, 40X – 18Y = 214.
What are:(i) the mean values X and Y,
(ii) the correlation coefficient between X and Y, and
(iii) the standard deviation of Y?
5 a) The following table gives, according to age, the frequency of marks obtained by 100 students in an intelligence test:
|
Age in years → Marks ↓ |
18 |
19 |
20 |
21 |
Total |
|
10–20 20–30 30–40 40–50 50–60 60–70 |
4 5 6 4 – – |
2 4 8 4 2 2 |
2 6 10 6 4 3 |
– 4 11 8 4 1 |
8 19 35 22 10 6 |
|
Total |
19 |
22 |
31 |
28 |
100 |
Calculate the Coefficient of Correlation between the Age and Marks.
b) An individual purchases three qualities of pencils. The relevant data are given below.
|
Quality |
Price per pencil (Rs.) |
Money spent (Rs.) |
|
A B C |
1.00 1.50 2.00 |
50 30 20 |
Calculate the average price per pencil.
6(a) An investigation of 23,713 households was made in an urban and rural mixed locality. Of these 1,618 were farmers, 2,015 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 of their family members as graduate. Obtain all the ultimate class frequencies.
(b) Investigate the association between darkness of eye-colour in father and son from the following data:
Fathers with dark eyes and sons with dark eyes: 50
Fathers with dark eyes and sons with not dark eyes: 79
Fathers with not dark eyes and sons with dark eyes: 89
Fathers with not dark eyes and sons with not dark eyes: 782
Also tabulate for comparison the frequencies that would have been observed had there been no heredity.
