Question

Find the mean deviation about the median for the given data.

$\begin{array}{cccccc}{x}_i& 15& 21& 27& 30& 35\\ f_i& 3& 5& 6& 7& 8\end{array}$

Answer 1

$\begin{array}{ccccc}{x}_i& f_i& e.f& |x_i-30|& f_i|x_i-30|\\ 15& 3& 3& 15& 45\\ 21& 5& 8& 9& 45\\ 27& 6& 14& 3& 18\\ 30& 7& 21& 0& 0\\ 35& 8& 29& 5& 40\\ & 29& & & 148\end{array}$

$\frac{N}{2}=\frac{29}{2}=14.5$

The e.f. just greater than 14.5 is 21 and corresponding value of x is 30.

$\therefore$ Median = 30

$\therefore$ M.D. about median = $\frac{1}{N}{\sum }_{i=1}^n{f}_i|x_i-M|=\frac{1}{29}\times 148=5.1$