Question

Find the mean deviation and coefficient of mean deviation from the following data

$\begin{array}{ccccccccc}X& 10& 12& 18& 23& 34& 45& 62& 75\end{array}$

Answer 1

Calculation of Mean Deviation from Arithmetic Mean and Coefficient of Mean Deviation

$\begin{array}{ccc}\text{S.No.}& \text{X}& |D|=(X-\overline{X})\\ & & |\overline{X}=34.8|\\ 1& 10& 24.8\\ 2& 12& 22.8\\ 3& 18& 16.8\\ 4& 23& 11.8\\ 5& 34& 0.8\\ 6& 45& 10.2\\ 7& 62& 27.2\\ 8& 75& 40.2\\ N=8& \sum X=279& \sum |D|=154.6\end{array}$

$\overline{X}=\frac{\sum X}{N}=\frac{279}{8}=34.8$

Mean Deviation $=\frac{\sum |D|}{N}=\frac{154.6}{8}=19.3$

$\therefore$ Coefficient of $MD=\frac{MD}{\overline{X}}=\frac{19.3}{34.8}=0.55$