Question

Find the co-efficient of correlation from following results: Average of x = 10.5, Average of y = 13.9, S.D. of x = 3.5, S.D. of Y = 4.1, ∑xy = 1364 and n = 10.​

Answer 1

Answer:

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Answer 2

Concept:

The strength of a linear link between two variables is measured by correlation coefficients. A positive association is shown by a correlation coefficient greater than zero, and a negative relationship is indicated by a number less than zero.

Given:

Average of x = 10.5.

Average of y = 13.9.

Standard deviation of x = 3.5

Standard deviation of x = 4.1

The sum of the products of x and y = 1364.

The number of terms = 10.

Find:

The coefficient of correlation.

Solution:

coefficient of correlation = $\frac{\frac{1}{n} [\sum xy - \bar{x} \bar{y}]}{S.D_x*S.D_y}$

                                         = $\frac{\frac{1}{10} [1364 - 10.5*13.9]}{3.5*4.1}$

                                          = $\frac{\frac{1}{10} [1364 - 142.95]}{14.35}$

                                          =$\frac{\frac{1}{10} [1218.05]}{14.35}$

                                          = 8.48

Hence, the coefficient of correlation is 8.48.