Calculation of Coefficient of Correlation

To calculate the coefficient of correlation, we need to first find the arithmetic means of the X and Y series.

Arithmetic Mean of X series:
The arithmetic mean of a series is the sum of all the values in the series divided by the number of values in the series.

Given X series: 6, 2, 10, 4, 8

Sum of X series = 6 + 2 + 10 + 4 + 8 = 30
Number of values in X series = 5

Arithmetic Mean of X series = Sum of X series / Number of values in X series
= 30 / 5
= 6

Therefore, the arithmetic mean of X series is 6.

Arithmetic Mean of Y series:
Given Y series: 9, 11, ?, 8, 7, 6 and 8

Sum of Y series = 9 + 11 + ? + 8 + 7 + 6 + 8 = 49 + ?
Number of values in Y series = 7

Arithmetic Mean of Y series = Sum of Y series / Number of values in Y series
= (49 + ?) / 7

Calculation of Coefficient of Correlation:
The coefficient of correlation (r) can be calculated using the formula:

r = Σ((X - X̄)(Y - Ȳ)) / √(Σ(X - X̄)^2 * Σ(Y - Ȳ)^2)

Where:
X is the individual value in X series
X̄ is the arithmetic mean of X series
Y is the individual value in Y series
Ȳ is the arithmetic mean of Y series

We need to calculate the value of r for each pair of X and Y values and then find the average of these values to get the coefficient of correlation.

Let's calculate the value of r for each pair of X and Y values:

r1 = (6 - 6)(9 - Ȳ) / (√((6 - 6)^2 * (9 - Ȳ)^2))
r2 = (2 - 6)(11 - Ȳ) / (√((2 - 6)^2 * (11 - Ȳ)^2))
r3 = (10 - 6)(? - Ȳ) / (√((10 - 6)^2 * (? - Ȳ)^2))
r4 = (4 - 6)(8 - Ȳ) / (√((4 - 6)^2 * (8 - Ȳ)^2))
r5 = (8 - 6)(7 - Ȳ) / (√((8 - 6)^2 * (7 - Ȳ)^2))
r6 = (8 - 6)(6 - Ȳ) / (√((8 - 6)^2 * (6 - Ȳ)^2))

To calculate the coefficient of correlation, we need to calculate the average of these values:

r = (r1 + r2 + r3 + r4 + r5 + r6) / 6

Once we calculate the value of r, we will have the coefficient of correlation.