Question

Calculate the mean deviation from the median of the following data.

$\begin{array}{cccccccc}\text{Class}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 4& 6& 10& 20& 10& 6& 4\end{array}$

Answer 1

Calculation of mean deviation from median,

$\begin{array}{cccccc}\text{Class}& \text{Mid~value(x\_i)}& Frequency\left(f_i\right)& \text{Cumulative frequency}& |d_i|=|x_i-45|& f_i|d_i|\\ 10-20& 15& 4& 4& 30& 120\\ 20-30& 25& 6& 10& 20& 120\\ 30-40& 35& 10& 20& 10& 100\\ 40-50& 45& 20& 40& 0& 0\\ 50-60& 55& 10& 50& 10& 100\\ 60-70& 65& 6& 56& 20& 120\\ 70-80& 75& 4& 60& 30& 120\\ & & \sum f_i=60& & & \sum f_i|d_i|=680\end{array}$

Here, $\sum f_i=N=60.$ So, $\frac{N}{2}=\frac{60}{2}=30$

The cumulative frequency just greater than 30 is 40 and the corresponding class is 40-50.

So, 40-50 is the median class.

l=40, cf=20, h=10 and f=20

Now, median $=1+\frac{\frac{N}{2}-cf}{f}\times h=40+\frac{30-20}{20}\times 10=40+5=45$

Mean deviation from median $=\frac{\sum f_i|d_i|}{\sum f_i}=\frac{680}{60}=1133$