Statistics - Pooled Variance (r)

Pooled Variance/Change is the weighted normal for assessing the fluctuations of two autonomous variables where the mean can differ between tests however the genuine difference continues as before.

Example

Problem Statement:

Compute the Pooled Variance of the numbers 1, 2, 3, 4 and 5.

Solution:

Step 1

Decide the normal (mean) of the given arrangement of information by including every one of the numbers then gap it by the aggregate include of numbers given the information set.

${Mean = frac{1 + 2 + 3 + 4 + 5}{5} = frac{15}{5} = 3 }$

Step 2

At that point, subtract the mean worth with the given numbers in the information set.

${Rightarrow (1 - 3), (2 - 3), (3 - 3), (4 - 3), (5 - 3) Rightarrow - 2, - 1, 0, 1, 2 }$

Step 3

Square every period s deviation to dodge the negative numbers.

${Rightarrow (- 2)^2, (- 1)^2, (0)^2, (1)^2, (2)^2 Rightarrow 4, 1, 0, 1, 4 }$

Step 4

Now discover Standard Deviation utipzing the underneath equation

${S = sqrt{frac{sum{X-M}^2}{n-1}}}$

Standard Deviation = ${frac{sqrt 10}{sqrt 4} = 1.58113 }$

Step 5

${Pooled Variance (r) = frac{((aggregate check of numbers - 1) imes Var)}{(aggregate tally of numbers - 1)} , \[7pt] (r) = (5 - 1) imes frac{2.5}{(5 - 1)}, \[7pt] = frac{(4 imes 2.5)}{4} = 2.5}$

Hence, Pooled Variance (r) =2.5