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Statistics – Pooled Variance (r)

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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 utilizing 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) times Var)}{(aggregate tally of numbers – 1)} , \[7pt]
(r) = (5 – 1) times frac{2.5}{(5 – 1)}, \[7pt]
= frac{(4 times 2.5)}{4} = 2.5}$

Hence, Pooled Variance (r) =2.5

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