Question

If the median of the following frequency distribution is 32.5. Find the values of f₁ and f2.

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	Total
Frequency	f1	5	9	12	f2	3	2	40

Answer 1

Given: Median = 32.5
We prepare the cumulative frequency table, as given below.

Class interval:	Frequency: (fi)	Cumulative frequency (c.f.)
0-10	f1	f1
10-20	5	5 + f1
20-30	9	14 + f1
30-40	12	26 +f1
40-50	f2	26 +f1 + f2
50-60	3	29 + f1 + f2
60-70	2	31 + f1 + f2
	N = 40 = 31 + f1 +f2

Now, we have
N = 40
31 + f₁ + f₂ = 40
f₂ = 9 - f₁    ........(1)

Also, `("N")/(2) = 20`

Since median = 32.5 so the median class is 30 - 40.
Here, l = 30, f = 12 , F = 14 + f₁ and h = 10

We know that

Median = `"l" + {{("N")/(2) -"F")/("f")} xx "h"`

`32.5 = 30 + {(20-(14+"f"_1))/(12)} xx 10`

`2.5 = ((6 - "f"_1) xx 10)/(12)`

2.5 x 12 = 60 - 10`"f"_1`

`"f"_1 = (30)/(10)`

= 3

Putting the value of `f_1` in (1), we get

`"f"_2` = 9 - 3

= 6
Hence, the missing frequencies are 3 and 6.