Calculation of Karl Pearson Coefficient of Correlation

Step 1: Calculate the mean of both the variables X and Y.

Mean of X = (42+44+58+55+89+98+61)/7 = 67.14

Mean of Y = (56+49+53+58+65+76+58)/7 = 60.14

Step 2: Calculate the deviations of X and Y from their respective means.

Deviation of X = (42-67.14), (44-67.14), (58-67.14), (55-67.14), (89-67.14), (98-67.14), (61-67.14)

= -25.14, -23.14, -9.14, -12.14, 21.86, 30.86, -6.14

Deviation of Y = (56-60.14), (49-60.14), (53-60.14), (58-60.14), (65-60.14), (76-60.14), (58-60.14)

= -4.14, -11.14, -7.14, -2.14, 4.86, 15.86, -2.14

Step 3: Calculate the product of deviations of X and Y.

Product of deviations of X and Y = (-25.14*-4.14), (-23.14*-11.14), (-9.14*-7.14), (-12.14*-2.14), (21.86*4.86), (30.86*15.86), (-6.14*-2.14)

= 104.2296, 257.194, 65.2596, 25.9396, 106.3096, 489.8296, 13.1096

Step 4: Calculate the square of deviations of X and Y.

Square of deviation of X = (-25.14)^2, (-23.14)^2, (-9.14)^2, (-12.14)^2, (21.86)^2, (30.86)^2, (-6.14)^2

= 632.2596, 534.7396, 83.5396, 147.6196, 477.1396, 951.1396, 37.6996

Square of deviation of Y = (-4.14)^2, (-11.14)^2, (-7.14)^2, (-2.14)^2, (4.86)^2, (15.86)^2, (-2.14)^2

= 17.1396, 123.8596, 51.1396, 4.5796, 23.6196, 251.4596, 4.5796

Step 5: Calculate the sum of square of deviations of X and Y.

Sum of square of deviation of X = 632.2596+534.7396+83.5396+147.6196+477.1396+951.1396+37.6996 =

Coefficient of Correlation (r) = + 0.88.