Question

How do you find the sum of deviations from mean?

Answer 1

Ways to find the sum of deviations:

1. Calculate the mean.

2. Subtract the mean from the individual values and write its modulus value to find deviations.

3. Add all the deviations.

For example: Suppose$5,7,10,16,20,26$are the data values.

Mean $=\frac{5+7+10+16+20+26}{6}$

$\begin{array}{rcl}& =& \frac{84}{6}\\ & =& 14\end{array}$

Sum of deviations $\begin{array}{rcl}& =& \left|5-14\right|+\left|7-14\right|+\left|10-14\right|+\left|16-14\right|+\left|20-14\right|+\left|26-14\right|\end{array}$

$\begin{array}{rcl}& =& \left|-9\right|+\left|-7\right|+\left|-4\right|+\left|2\right|+\left|6\right|+\left|12\right|\\ & =& 9+7+4+2+6+12\\ & =& 40\end{array}$

Hence, the sum of deviations of the given data set is 40.