Statistics - Variance


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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 −

  • ${M}$ = Mean of items.

  • ${n}$ = the number of items considered.

  • ${n_i}$ = 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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