Question

Calculate the median from the following frequency distribution:
$\begin{array}{ccccccccc}\text{Class}& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40& 40-45\\ \text{Frequency}& 5& 6& 15& 10& 5& 4& 2& 2\end{array}$

• A.
  16.5
• B.
  17.5
• C.
  18.5
• D.
  19.5

Answer 1

The correct option is D

19.5

We prepare the cumulative frequency table, as shown:

Class	$f_i$	$c{f}_i$
5-10	5	5
10-15	6	11
15-20	15	26
20-25	10	36
25-30	5	41
30-35	4	45
35-40	2	47
40-45	2	49
	Σ$f_i$ = 49

N = Σ$f_i$ = 49

⇒ N/2 = 24.5

The cumulative frequency greater than 24.5 is 26 and the corresponding class is 15-20.

Thus the median class is 15-20.

Therefore, $l$= 15, $h$ = 5,
$f$ = 15,
c.f. of preceding class = 11 and N/2 = 24.5

Median,
M = $l$ + ((N/2 − $cf$)/$f$) × $h$

Median = 15 + ((24.5 – 11)/15) × 5

Median = 15 + 4.5

Median = 19.5

Hence, median is 19.5 .