Find the sum of the deviations of the variate values 3, 4, 6, 7, 8, 14 from their mean.

Given:

3, 4, 6, 7, 8, 14

To do:

We have to find the sum of the deviations of the variate values 3, 4, 6, 7, 8, 14 from their mean.

Solution:

We know that,

Mean $\overline{X}=\frac{Sum\ of\ the\ observations}{Number\ of\ observations}$

Therefore,

Mean of 3, 4, 6, 7, 8, 14 $=\frac{3+4+6+7+8+14}{6}$

$=\frac{42}{6}$

$=7$

$\bar{x}=7$

$\sum_{i=1}^{n}(x_{i}-\bar{x})=0$

Sum $=(3-7)+(4-7)+(6-7)+(7-7)+(8-7)+(14-7)$

$=3+4+6+7+8+14-6 \times 7$

$=42-42$

$=0$

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Updated on: 10-Oct-2022

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