Question

Find the mean deviation about median for the following data

$\begin{array}{ccccccc}Marks& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ No.ofgirls& 4& 8& 9& 10& 7& 5\end{array}$

Answer 1

$\begin{array}{cccccc}Marks& MidValues{x}_1& f_i& cf& |x_i-M|& f_i|x_i-M|\\ 0-10& 5& 6& 6& 22.86& 137.16\\ 10-20& 15& 8& 14& 12.86& 102.88\\ 20-30& 25& 14& 28& 2.86& 40.04\\ 30-40& 35& 16& 44& 7.14& 114.24\\ 40-50& 45& 4& 48& 17.14& 68.56\\ 50-60& 55& 2& 50& 27.14& 54.28\\ & & 50& & & 517.16\end{array}$

Here, N/2 = 50/2 = 25

Median Class = 20 – 30

So, Median $=l+\left(\frac{\frac{N}{2}+f_0}{f_m}\right)\times c$
$=20+\frac{25-14}{14}\times 10=20+7.86=27.86$
Mean Deviation about median $=\frac{1}{N}{\sum }_{i=1}^n{f}_i|x_i-M|=\frac{1}{50}\times 517.16=10.37$