Page 184 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes N åå f u v - (å f u )(å f v ¢ )
r = ij i j i i j j
N å f u - (å f u ) N å f v - (å f v ¢ )
XY 2 2
¢
2
2
i i i i j j j j
Example: Calculate Karl Pearson’s coefficient of correlation from the following data:
Age (yrs.)  18 19 20 21 22
Marks 

20 - 25 3 2
15 - 20 5 4
10 - 15 7 10
5 - 10 3 2
0 - 5 4
Solution:

Let X denote the mid-value of the class interval of marks. Various values of X can be written as
i i
22.5, 17.5, 12.5, 7.5 and 2.5.
Further, let u = (X – 12.5) ÷ 5. Various values of u would be 2, 1, 0, – 1 and – 2.
i i i
Similarly, let Y denote age. Various values of Y are 18, 19, 20, 21 and 22.
j j
Assuming v = Y – 20, various values of v would be – 2, – 1, 0, 1 and 2.
j j j
We shall use the values of u and v in the computation of r.
i j
Table for Calculation of r

Substituting various values in the formula for r, we get

40 ´ ( 44- ) 6 12- ´ - 1832
r = = = - 0.903
-
´
-
´
40 50 36 40 56 144 1964 2096

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