# From the information below determine the variance:- 1754, 1633,1502, 1476,1846 and 1478

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### 1 Answer

You need to perform the following steps to evaluate the variance, such that:

- average the given numbers

- square the number resulted when subtract the mean from each number

- average the squares resulted

You should evaluate first the mean of numbers, such that:

`M = (1754 + 1633 + 1502 + 1476 + 1846 + 1478)/6`

`M = 9689/6 = 1614.83 ~~ 1614`

You need to subtract the mean, `M = 1614` , from each number, such that:

`1754 - 1614 = 140`

`1633 - 1614 = 19`

`1502 - 1614 = -112`

`1476 - 1614 = -138`

`1846 - 1614 = 232`

`1478 - 1614 = -136`

You need to evaluate the variance `sigma` , averaging the squares of differences above, such that:

`sigma = (140^2 + 19^2 + (-112)^2 + (-138)^2 + 232^2 + (-136)^2)/6`

`sigma = (19600 + 361 + 12544 + 19044 + 53824 + 18496)/6`

`sigma = 123869/6`

`sigma = 20644.83`

**Hence, evaluating the variance, using the data provided by the problem, yields `sigma = 20644.83` .**