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Look at the frequency distribution table given below:

Class Interval
Frequency
35-45
8
45-55
12
55-65
20
65-75
10

The median of the above distribution is

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56.5

57.5

58.5

answer is B.

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Detailed Solution

The given frequency distribution table is:

Class Interval	Frequency
35-45	8
45-55	12
55-65	20
65-75	10

Formula used for median:

M e d i a n = l + h × N 2 − c f f

,
where,

l

=lower limit of the median class,

h

=size of the median class,

f

= frequency of the median class,

N

= sum of frequencies and

c f

=cumulative frequency of the class just preceding the median class.
The frequency distribution table will be,

Class Interval	Frequency	Cumulative Frequency
35-45	8	8
45-55	12	8+12=20
55-65	20	20+20=40
65-75	10	40+10=50

Here,

N 2 = 502 = 25

.
The cumulative frequency just greater than 25 is 40 and the corresponding class is

55 − 65

.
Therefore, the median class is

55 − 65

∴ l = 55, h = 10, f = 20, N = 50 and c f = 20

Calculating the median, we get,

Median = l + h × N 2 − c f f Median = 55 + 10 × 502 − 20 20 Median = 55 + 10 × 25 − 20 20 Median = 55 + 10 × 520 M e d i a n = 55 + 10 × 0.25 M e d i a n = 55 + 2.5 M e d i a n = 57.5

Therefore, the median is 57.5.
Thus, the correct answer is option 2.

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