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Which of the following is the median for the following data?

Class
Frequency(f)
Cumulative frequency(cf)
18.5-25.5
35
35
25.5-32.5
96
131
32.5-39.5
68
199
39.5-46.5
102
301
46.5-53.5
35
336
53.5-60.5
4
340

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36.51

35.61

35.51

31.61

answer is A.

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Detailed Solution

Consider the given table,

Class	Frequency(f)	Cumulative frequency(cf)
18.5-25.5	35	35
25.5-32.5	96	131
32.5-39.5	68	199
39.5-46.5	102	301
46.5-53.5	35	336
53.5-60.5	4	340
	$N = \sum f = 340$

Here, we have,
N=

\sum f

= 340

\frac{N}{2} = \frac{340}{2}

= 170
We can observe that the cumulative frequency just greater than 170 is 199 and the corresponding class is

32.5 − 39.5

.
Therefore, the median class is

32.5 − 39.5

.
We know that 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 of the class just preceding the median class.
Note that, here

l = 32.5

N = 340

f = 68

h = 7

c . f = 131

Therefore, the median is,

= 32.5 + 7 × 170 − 131 68 = 32.5 + 4.01 = 36.51

Hence, the value of median is 36.51.
Therefore, option 1 is correct.

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