Question

Find the median for the following grouped data.

Class - Interval	Frequency
$1-5$	$4$
$6-10$	$3$
$11-15$	$6$
$16-20$	$5$
$21-25$	$2$
	$N=20$

Answer 1

Median is the middle score. Here actual scores are not given. So we have to use to different procedure to find the median. We have $N=20$, an even number. Therefore, there are two middle scores: one corresponding to $N/2=20/2=10th$ score and the other is $11th$ score.
We have to locate the median between $10th$ and $11th$ scores. Since we are not given individual scores, we have to get some idea about $10th$ and $11th$ scores. For this it is required to find the cumulative frequency.
Observe the following table, to know how to find cumulative frequency.

Class Interval	Frequency (f)	Cumulative frequency $\left(f_c\right)$
$1-5$	$4$	$4$	$4$
$6-10$	$3$	$7$	$4+3=7$$
$11-15$	$6$	$13$	$7+6=13$
$16-20$	$5$	$18$	$13+5=18$
$21-25$	$2$	$20$	$18+2=20$
	$N=20$