If the median of the following frequency distribution is 32.5, find the values of f1 and f2
Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | Total |
Number of batsmen | f1 | 5 | 9 | 12 | f2 | 3 | 2 | 40 |
Given: Median = 32.5 & N = 40
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 | NUMBER OF BATSMEN(fi) | Cf |
0 - 10 | f1 | f1 |
10 - 20 | 5 | 5 + f1 |
20 - 30 | 9 | 5 + f1 + 9 = 14 + f1 |
30 - 40 | 12 | 14 + f1 + 12 = 26 + f1 |
40 - 50 | f2 | 26 + f1 + f2 |
50 - 60 | 3 | 26 + f1 + f2 + 3 = 29 + f1 + f2 |
60 - 70 | 2 | 29 + f1 + f2 + 2 = 31 + f1 + f2 |
TOTAL | 31 + f1 + f2 |
Median = 32.5 (as already mentioned in the question)
32.5 lies between 30 - 40 ⇒ Median class = 30 - 40
∴ l = 30, h = 10, f = 12, N/2 = (31 + f1 + f2)/2 = 40/2 and Cf = 14 + f1
Median is given by,
⇒ 
⇒ 
⇒ 32.5 – 30 = (60 – 10f1)/12
⇒ (2.5)(12) = 60 – 10f1
⇒ 30 = 60 – 10f1
⇒ f1 = 3 …(i)
And given that N = 40
⇒ 31 + f1 + f2 = 40
⇒ f1 + f2 = 9 …(ii)
Substituting f1 = 3 in eq.(ii),
3 + f2 = 9
⇒ f2 = 6
Thus, the unknown frequencies are f1 = 3 and f2 = 6.