Question

Write the median clas of the following distribution:

$\begin{array}{cccccccc}Class& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ Frequency& 4& 4& 8& 10& 12& 8& 4\end{array}$

Answer 1

Class	Mid-point(x)	Frequency(f)	($f_x$)	Cumulative frquency
0-10	5	4	20	4
10-20	15	4	60	4+4=8
20-30	25	8	200	8+8=16
30-40	35	10	350	16+10=26
40-50	45	12	540	26+12=38
50-60	55	8	440	38+8=46
60-70	65	4	260	46+4=50
		∑f = 50	∑($f_x$) = 1870

Mean = $\frac{\sum f_x}{\sum f}=\frac{1870}{50}$ = 37.4

A median group is in the range of 30 - 40, as we have mean 37.4

And
Formula for median = $L+\frac{\frac{N}{2}-C{f}_b}{f_m}\times w$
Here
L is the lower class boundary of the group containing the median = 30
n is the total number of data = 50
c ($f_b$) is the cumulative frequency of the groups before the median group = 16
($f_m$) is the frequency of the median group = 10
w is the group width = 10
So,
Median = $30+\frac{\frac{50}{2}-16}{10}\times 10$ = 30+ 25 - 16 = 39