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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