Question

With mean as the base, calculate the mean deviation and compare the variability of the two series A and B.

$\begin{array}{cccccccc}\text{Series A}& 10& 12& 16& 20& 25& 27& 30\\ \text{Series B}& 10& 20& 22& 25& 27& 31& 40\end{array}$

Answer 1

$\begin{array}{cccc}\text{Series A}& \text{Deviations from Mean}& \text{Series B}& \text{Deviations from Mean}\\ X_A& X_A-{\overline{X}}_A& X_B& X_B-{\overline{X}}_B\\ & |D|& & |D|\\ 10& 10& 10& 15\\ 12& 8& 20& 5\\ 16& 4& 22& 3\\ 20& 0& 25& 0\\ 25& 5& 27& 2\\ 27& 7& 31& 6\\ 30& 10& 40& 15\\ \sum X_A=140& \sum |D|=44& \sum X_B=175& \sum |D|=46\end{array}$

Series A:-

Mean $={\overline{X}}_A=\frac{\sum X_A}{N}=\frac{140}{7}=20$

Mean Deviation (Series A) = $\frac{\sum |D|}{N}=\frac{44}{7}=6.28$

Coefficient of M.D (Series A) = $\frac{M.D}{{\overline{X}}_A}=\frac{6.28}{20}=0.31$

Series B:-

Mean $={\overline{X}}_B=\frac{\sum X_B}{N}=\frac{175}{7}=25$

Mean Deviation (Series B) = $\frac{\sum |D|}{N}=\frac{46}{7}=6.57$

Coefficient of M.D (Series B) = $\frac{M.D}{{\overline{X}}_B}=\frac{6.57}{25}=0.26$

Since coefficient of mean deviation for series A is more than that of series B, we can say that series A has greater variability as compared to series B.