Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
Frequency | 5 | 25 | ? | 18 | 7 |
Median(given) = 24, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table, where x is the unknown frequency.
CLASS | FREQUENCY(fi) | Cf |
0 - 10 | 5 | 5 |
10 - 20 | 25 | 5 + 25 = 30 |
20 - 30 | x | 30 + x |
30 - 40 | 18 | 30 + x + 18 = 48 + x |
40 - 50 | 7 | 48 + x + 7 = 55 + x |
TOTAL | 55 + x |
Median = 24 (as already mentioned in the question)
24 lies between 20 - 30 ⇒ Median class = 20 - 30
∴ l = 20, h = 10, f = x, N/2 = (55 + x)/2 and Cf = 30
Median is given by,
⇒ 
⇒ 
⇒ 24 – 20 = (10x – 50)/2x
⇒ (4)(2x) = 10x – 50
⇒ 8x = 10x – 50
⇒ 10x – 8x = 50
⇒ 2x = 50
⇒ x = 25
Thus, the unknown frequency is 25.