If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of

f
1

and
f
2

are ____ and ____, respectively.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702

Question

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of

f
    1
   
    and 
    f
    2

are ____ and ____, respectively.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702

Infinity Learn · Accepted Answer

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of

f_{1}

and

f_{2}

are 3 and 6, respectively.

Given that the median of the following frequency distribution is 32.5 and the sum of frequencies is 40.

The cumulative frequency distribution will be:

The formula for median:

M = l + h × N 2 − c f f

where,

l =

the lower limit of the median class,

N = ∑ frequency

, and

cf =

cumulative frequency.

f 1 + f 2 + 31 = 40 f 1 + f 2 = 9 f 2 = 9 − f 1

The median is 32.5 which lies in class interval

30 − 40

.
Hence, the median class

= 30 − 40

.
So,

l = 30, N 2 = 402 = 20, f = 12,

and

c f = 14 + f 1

Substituting values in formula of median, we get:

30 + 20 − 14 + f 1 12 × 10 = 32.5 6 − f 1 12 × 10 = 2.5 6 − f 1 = 3 f 1 = 3

Substitute the value of

f 1

in

f 2 = 9 − f 1

,

⇒ f 2 = 9 − 3 ⇒ f 2 = 6

Hence, the values of

f 1

and

f 2

are

3

and

6

respectively.

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of $f 1 and f 2$ are and , respectively.

Class Interval
Frequency
0-10
$f_{1}$
10-20
5
20-30
9
30-40
12
40-50
$f_{2}$
50-60
3
60-70
2