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TUTOR MARKED ASSIGNMENT
MST-002: Descriptive Statistics
Course Code: MST-002
Assignment Code: MST-002/TMA/2024
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. (2×5=10)
a) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
b) Mean deviation is least when calculated from the median.
c) The correlation coefficient between x and (a – x) is –1.
d) The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
e) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.
2.
a) Find the missing information from the following data:
Group I Group II Group III Combined
Number 50 ? 90 200
Standard Deviation 6 7 ? 7.746
Mean 113 ? 115 116
b) If AM and GM of two numbers are 30 and 18, respectively, find the numbers. (7+3)
3.
a) The frequency distribution of the marks obtained by the 25 students each of the two sections is given as follows:
Marks: 10-20 20-30 30-40 40-50 50-60
Section A: 2 5 10 5 3
Section B: 3 7 8 5 2
Find which section is more consistent.
b) Mean and Standard deviation of 18 observations are found to be 7 and 4, respectively. On comparing the original data, it was found that an observation 12 was miscopied as 21 in the calculations. Calculate correct mean and standard deviation. (7+3)
4.
The equations of two regression lines are given as follows:
4x – 5y + 30 = 0
20x−9y – 107 = 0
Calculate (i) regression coefficients, byx and bxy; (ii) correlation coefficient r(x, y); (iii) Mean of X and Y; and (iv) the value of σy if σx = 3. (10)
5.
A researcher collects the following information for two variables x and y:
n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, σx = 4 and σy = 5
Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y). (10)
6.
a) If a, b, c, d are constants, then show that the coefficient of correlation between ax+b and cy+d is numerically equal to that between x and y.
b) A statistician wanted to compare two methods A and B of teaching. He selected a random sample of 22 students. He grouped them into 11 pairs so that the students in pair have approximately equal scores on an intelligence test. In each pair one student was taught by method A and the other by method B and examined after the course. The marks obtained by both methods are given as:
Methods 1 2 3 4 5 6 7 8 9 10 11
Method A 24 29 19 14 30 19 27 30 20 28 11
Method B 37 35 16 26 23 27 19 20 16 11 21
Find the rank correlation coefficient. (3+7)
7.
a) Fit an exponential curve of the form 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) Calculate the first, second and third quartile for the following data:
Class: Below 30 30-40 40-50 50-60 60-70 70-80 80 and above
Frequency: 69 167 207 65 58 27 10
Also find the quartile deviation and coefficient of quartile deviation. (10+10)
8.
a) Board of Directors of Labour Union wishes to sample the opinion of its members before submitting a change in its contribution at a forthcoming annual meeting. Questionnaires are sent to a random sample of 200 members in three union locals. The results of the survey are as follows:
Union Locals
Reaction A B C Total
Favour Change 35 45 20 100
Against Change 15 25 16 56
No Response 10 10 24 44
Total 60 80 60 200
Determine the amount of association between the Union locals and their reactions using coefficient of contingency and interpret the result.
b) 600 candidates were appeared in an examination. The boys outnumbered girls by 15% of all candidates. Number of passed exceeded the number of failed candidates by 300. Boys failing in the examination numbered 80. Determine the coefficient of association. (12+8)
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