Question

7. Given X = 125. SY = 100, X2 = 650, Y2 = 436, XY = 520, n= 25,
Obtain the value of Karl Pearson's correlation coefficient.
0.65
0.67
O 0.66​

Answer 1

Answer:

0.66 ufudugjdtdkbdys0ugo7dId0jgkh

Answer 2

Given

• ΣX = 125
• ΣY = 100
• ΣY^2 = 436
• ΣX^2 = 650
• ΣXY = 520
• n= 25

To find

• Karl Pearson's correlation coefficient.

Solution

Karl Pearson's correlation coefficient is the measure of the degree of relationship between two variables.

It is given by,

$r = \frac{cov(x, y)}{sd(x) \times sd(y)}$

cov(x,y) = 1/n ΣXY - xy

where x and y are mean x and y.

mean x = 1/25 [125] = 5

mean y = 1/25[100] = 4

cov (x,y) = 1/25 (520) - 5×4

or, cov (x,y) = 1/25 (520) -20

or, cov (x,y) = 20.8-20

or, cov (x,y) = 0.8

SD(X) = 1/25 [650] - 5^2

or, SD(X) = 26-25

or, SD(X) = 1

SD(Y) = 1/25[436]- 4^2

or,SD(Y) = 17.44 - 16

or, SD(Y) = 1.44

Therefore, r = 0.8 /[1×1.44]

or, r = 0.8/1.44

or, r = 0.55