Question

Calculate the median from the following data:

Marks	0 – 10	10 – 30	30 – 60	60 – 80	80 – 90
Number of students	5	15	30	8	2

Answer 1

Calculate the median from the given data:

The cumulative frequency table:

Marks	Number of students	Cumulative frequency
0 – 10	5	5
10 – 30	15	5 + 15 = 20
30 – 60	30	20 + 30 = 50
60 – 80	8	50 + 8 = 58
80 – 90	2	58 + 2 = 60

Here $N=60$

∴ $$\begin{gathered} N=\frac{60}{2} \\ =30 \end{gathered}$$

The cumulative frequency ($c.f$) just greater than $30$ is $50$.

The corresponding class (Median class)$=30-60$

• $l=30$
• $c.f=30$
• $F=30$
• $h=30$

$Median=l+\frac{{\displaystyle \frac{n}{2}}-F}{c.f}\times h$

$Median=30+\frac{{\displaystyle 30}-20}{30}\times 30$

Median $=40$

Hence , the required median is $40$ .