Question

Calculate the mean deviation of the following income groups of five and seven members from their medians :

$\begin{array}{cc}\text{I}& \text{II}\\ \text{Income in Rs}& \text{Income in Rs}\\ 4000& 3800\\ 4200& 4000\\ 4400& 4200\\ 4600& 4400\\ 4800& 4600\\ & 4800\\ & 5800\end{array}$

Answer 1

Calculate the mean deviation for the first data set. The data is already arranged in ascending order.

For this data set, n is equal to 5.

Also, median, M = 4400

$\begin{array}{cc}{x}_i& |d_i|=|x_i-M|\\ 4000& 400\\ 4200& 200\\ 4400& 0\\ 4600& 200\\ 4800& 400\\ \text{Total}& 1200\end{array}$

$M.D.=\frac{1}{5}\times 1200=240$

Therefore, for the income of families in the first group, the mean deviation from the median is Rs 240.

Now, consider the second data set. This is also arranged in ascending order.

Here, n = 7

Also, median M = 4400

$\begin{array}{cc}{x}_i& |d_i|=|x_i-M|\\ 3800& 600\\ 4000& 400\\ 4200& 200\\ 4400& 0\\ 4600& 200\\ 4800& 400\\ 5800& 1400\\ \text{Total}& 3200\end{array}$

$M.D.=\frac{1}{7}\times 3200=457.14$