Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.19

SELF EXAMINATION QUESTIONS (Theory)
Problem 1. Define correlation explain various types of correlation with suitable example.
Problem 2. State any two of the properties of Pearson’s coefficient of correlation.
Problem 3. What is rank correlation explain with the help of an example.

UNSOLVED PROBLEMS (PRACTICAL)
Problem 4. Find correlation coefficient between the variable X and Y

X 80 86 34 56 76 89 65 45 54 15

Y 25 35 40 54 44 25 21 28 20 28

[Ans. r = –0.047]
Problem 5. Find correlation between age of husband and wife

Age of husband 80 45 55 56 58 60 65 68 70

Age of wife 82 56 50 48 60 62 64 65 70

(Ans. r = 0.862)

Problem 6. The total of the multiplication of deviation of X and Y = 3044
No. of pairs of the observations is 10
Total of deviation of X = (-)170
Total of deviations of Y = (-)20
Total of squares of deviations of X = 8281
Total of squares of deviations of Y = 2264
Find out the coefficient of correlation when the arbitrary means of X and Y are 82 and 68 respectively.
(Ans.: r = 0.781, hint: arbitrary mean are not required for the solution)

Problem 7. Calculate coefficient of correlation from the following data and comment on the result.

Experience X 16 12 18 4 3 10 5 12

Performance Y 23 22 24 17 19 20 18 21

(Ans. 0.951)

Problem 8. Calculate rank correlation coefficient between two seris X and Y, given below –

X 70 65 71 62 58 69 78 64

Y 91 76 65 83 90 64 55 48

(Ans. -0.309)

Problem 9. Calculate rank correlation coefficient from the data given below –

X 75 88 95 70 60 80 81 50

Y 120 134 150 115 110 140 142 100

(Ans. 0.929)