Question

Calculate the mean deviation about the median for the following data.
$\begin{array}{ccccccccc}Marks& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ No.ofstudents& 18& 16& 15& 12& 10& 5& 2& 2\end{array}$

Answer 1

$\begin{array}{cccccc}Class& f& c.f.& Mid-markx& |x-M|& f|x-M|\\ 0-10& 18& 18& 5& 19& 342\\ 10-20& 16& 34& 15& 9& 144\\ 20-30& 15& 49& 25& 1& 15\\ 30-40& 12& 61& 35& 11& 132\\ 40-50& 10& 71& 45& 21& 210\\ 50-60& 5& 76& 55& 31& 155\\ 60-70& 2& 78& 65& 41& 82\\ 70-80& 2& 80& 75& 51& 102\\ & 80& & & & 1182\end{array}$
$\frac{N}{2}=40$
Median class is 20-30
$\therefore$ l = 20, N=80, C=34, f=15, h=10.
$Median=l+\left(\frac{\frac{N}{2}-C}{f}\right)\times h$
$=20+\frac{40-34}{15}\times 10$
$=20+\frac{6}{15}\times 10$
$=24$
Mean deviation about $M==\frac{{\sum }_{i=1}^n{f}_i|x_i-M|}{N}=\frac{1192}{80}=14.775$.