How to Calculate Pooled Variance (r) ? - Tutorial

Definition:

Pooled variance is the weighted average for evaluating the variances of two independent variables where the mean can vary between samples but the true variance remains the same.

Example :

Calculate the variance of the numbers 1, 2, 3, 4, 5

Solution :

Step 1:

Determine the average (mean) of the given set of data by adding all the numbers then divide it by the total count of numbers given in the data set. Mean = (1 + 2 + 3 + 4 + 5) / 5 = (15) / 5 = 3

Step 2:

Then, subtract the mean value with the given numbers in the data set. =>(1 - 3), (2 - 3), (3 - 3), (4 - 3), (5 - 3) => -2, -1, 0, 1, 2

Step 3:

Square each period's deviation to avoid the negative numbers. =>(-2)², (-1)², (0)², (1)², (2)² => 4, 1, 0, 1, 4

Step 4:

Now, let us find the Standard Deviation for the given numbers (1, 2, 3, 4, 5) Find the sum of (number-Mean)² 4 + 1 + 0 + 1 + 4 = 10 The total number of value is 5. So N=5 Find N - 1 5 - 1 = 4 Now find Standard Deviation using the below formula.

Standard Deviation = √10 / √4 = 1.58113

To find the Variance

After finding the standard deviation square the values. (1.58113)² = 2.4999 Therefore, the value of Variance = 2.5

Step 5:

Pooled Variance (r) = ( (total count of numbers -1) * Var ) / (total count of numbers - 1)

(r) = (5 - 1) * (2.5) / (5 - 1)
    = (4 * 2.5) / 4
    = 2.5 Hence, Pooled Variance (r) = 2.5