Question

Calculate the median from the following data:

Marks below:	10	20	30	40	50	60	70	80
No. of students	$15$	$35$	$60$	$84$	$96$	$127$	$198$	$250$

Answer 1

Marks (x)	No. of students (f)	C.F.
0-10	15	15
10-20	20	35
20-30	25	60
30-40	24	84
40-50	12	96
50-60	31	127
60-70	71	198
70-80	52	250
	N = 250

As, $N=250\Rightarrow \frac{N}{2}=\frac{250}{2}=125$

As $127$ is just greater than $125,$ therefore median class is $50-60$.

$Median=l+\frac{\frac{N}{2}+C}{f}\times h$

Here, $l=$lower limit of median class $=50$

$C=C.F.$ of the class preceding the median class $=96$

$h=$ higher limit - lower limit $=60-50=10$

$f=$ frequency of median class $=31$

$\therefore median=50+\frac{125-96}{31}\times 10=50+9.35=59.35$