Page 188 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 8: Correlation Analysis

7. Calculate Karl Pearson’s coefficient of correlation between the marks obtained by Notes
10 students in economics and statistics.

Roll No. : 1 2 3 4 5 6 7 8 9 10
Marks in eco. : 23 27 28 29 30 31 33 35 36 39
Marks in stat. : 18 22 23 24 25 26 28 29 30 32
8. Find Karl Pearson’s coefficient of correlation from the following data and interpret its
value.
: 100 101 103 102 100 99 97 98 96 95
: 98 99 99 97 95 92 95 94 90 91
9. Find the coefficient of correlation between X and Y. Assume 69 and 112 as working origins
for X and Y respectively.
X : 78 89 96 69 59 79 68 61
Y : 125 137 156 112 107 136 123 108
10. (a) Calculate the coefficient of correlation from the following data and interpret the
result.

XY 8425, X 28.5, Y 28.0, 10.5, 5.6, and n 10
X Y
(b) Draw a scatter diagram of the following data and indicate whether the correlation
between the variables is positive or negative.
Height (inches) : 62 72 70 60 67 70 64 65 60 70
Weight (lbs.) : 50 65 63 52 56 60 59 58 54 65
11. The coefficient of rank correlation of the marks obtained by 10 students in biology and
chemistry 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 wrongly taken as 2 instead of 5. Find the
correct value of coefficient of correlation.

12. Rank correlation coefficient for a certain number of pairs of observations was found to be
0.75. If the sum of squares of the differences between the corresponding ranks is 91, find
the number of pairs.
13. Coefficient of rank correlation and the sum of squares of differences in corresponding
ranks are 0.9021 and 28 respectively. Determine the number of pairs of observations.

Answers: Self Assessment

1. Univariate Distribution 2. Bivariate Distribution
3. association 4. Correlation
5. covariation 6. ’degree of relationship’
7. Correlation Coefficient 8. high

9. –1,+1 10. scatter diagram
11. (d) 12. (a)
13. (b) 14. (a)
15. (a)

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