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A variance is defined as the average of Squared differences from mean value.
Combination is defined and given by the following function:
Formula
${ delta = frac{ sum (M – n_i)^2 }{n}}$
Where −
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${M}$ = Mean of items.
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${n}$ = the number of items considered.
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${n_i}$ = items.
Example
Problem Statement:
Find the variance between following data : {600, 470, 170, 430, 300}
Solution:
Step 1: Determine the Mean of the given items.
${ M = frac{600 + 470 + 170 + 430 + 300}{5} \[7pt]
= frac{1970}{5} \[7pt]
= 394}$
Step 2: Determine Variance
${ delta = frac{ sum (M – n_i)^2 }{n} \[7pt]
= frac{(600 – 394)^2 + (470 – 394)^2 + (170 – 394)^2 + (430 – 394)^2 + (300 – 394)^2}{5} \[7pt]
= frac{(206)^2 + (76)^2 + (-224)^2 + (36)^2 + (-94)^2}{5} \[7pt]
= frac{ 42,436 + 5,776 + 50,176 + 1,296 + 8,836}{5} \[7pt]
= frac{ 108,520}{5} \[7pt]
= frac{(14)(13)(3)(11)}{(2)(1)} \[7pt]
= 21,704}$
As a result, Variance is ${21,704}$.
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