Question

Find the median for the following frequency distribution table :

Class- interval	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30
frequency	5	3	9	10	8	5

Answer 1

Given distribution

Class-interval $0-5$ $5-10$ $10-15$ $15-20$ $20-25$ $25-30$

Frequency $5$ $3$ $9$ $10$ $8$ $5$

Now we can prepare a table for calculating median

Class-interval Frequency Cumulative frequency

$0-5$ $5$ $5$

$5-10$ $3$ $5+3=8$

$10-15$ $9$ $8+9=17$(c.l)

$15-20$ $10$ $17+10=27$

$20-25$ $8$ $27+8=35$

$25-30$ $5$ $35+5=40$

$N=40$

$\Rightarrow N/2=40/2=20$

then the median class;

$15-20$

Lowest limit(l)$=15$

Class width(h)$=5$

Frequency(f)$=10$

and c.f$=$ preceding cumulative frequency of median class

$=$median

$=l+\left(\frac{N/2-c.f}{f}\right)\times h$

$=15+\left(\frac{20-17}{10}\right)\times 15$

$=15+\frac{3\times 5}{10}=15+\frac{15}{10}$

Median$=15+1.5=16.5$.