Question

Find out mean deviation and coefficient of mean deviation, using arithmetic mean from the following data:

$\begin{array}{cccccc}\text{Profit (Rs)}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Shops (Number)}& 5& 10& 15& 20& 25\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Profit}& \text{Mid-value}& \text{Frequency}& \text{Multiple of}& \text{Deviation from}& \text{Multiple of}\\ \text{(Rs)}& \text{(m)}& \text{(f)}& \text{Mid-value and}& \text{Mean}& \text{Deviation and the}\\ & & & \text{Frequency}& |d\overline{x}|=|m-\overline{X}|& \text{Corresponding to}\\ & & & \text{(fm)}& \overline{X}=31.66& \text{Frequency}\left(f|d\overline{x}|\right)\\ 0-10& 5& 5& 25& 26.66& 133.30\\ 10-20& 15& 10& 150& 16.66& 166.60\\ 20-30& 25& 15& 375& 6.66& 99.90\\ 30-40& 35& 20& 700& 3.34& 66.80\\ 40-50& 45& 25& 1,125& 13.34& 333.50\\ & & \sum \text{f}=75& \sum \text{fm}=2,375& \sum |d\overline{x}|=66.66& \sum \text{f}|d\overline{x}|=800.10\end{array}$

$\overline{X}=\frac{\sum \text{fm}}{\sum \text{f}}=\frac{2,375}{75}=31.66$

Mean Deviation from Arithmetic Mean

${\text{MD}}_{\overline{X}}=\frac{\sum \text{f}|d\overline{x}|}{\sum \text{f}}=\frac{800.10}{75}=10.67$

Coefficient of Mean Deviation

$=\frac{M{D}_{\overline{X}}}{\overline{X}}=\frac{10.67}{31.67}=0.34$

Mean Deviation = 10.67, Coefficient of Mean Deviation = 0.34.