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In a hospital, the ages of diabetic patients were recorded as follows.

Age (in years)
No. of patients
0-15
5
15-30
20
30-45
40
45-60
50
60-75
25

The median age is ____ years.

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Detailed Solution

In a hospital, the ages of diabetic patients were recorded as follows.

Age (in years)	No. of patients
0-15	5
15-30	20
30-45	40
45-60	50
60-75	25

The median age is 46.5 years.
Given:

Age (in years)	No. of patients
0-15	5
15-30	20
30-45	40
45-60	50
60-75	25

Formula used:

Median = 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 =

the sum of frequencies and

c . f .

cumulative frequency of the class just preceding the median class.
The cumulative frequency table:

Age (in years)	No. of patients	Cumulative Frequency
0-15	5	5
15-30	20	5+20=25
30-45	40	25+40=65
45-60	50	65+50=115
60-75	25	105+25=140

Here,

N = 140 ⇒ N 2 = 1402 ⇒ N 2 = 70

The cumulative frequency just greater than 70 is 115 and the corresponding class is 45-60.
Therefore, the median class is 45-60.

∴ l = 45, h = 15, f = 50, N = 140 and c f = 65

Substitute the values in the formula:

∴ Median = l + N 2 − c f f × h ⇒ Median = 45 + 70 − 65 50 × 15 = 45 + 1.5 = 46.5

Hence, the median age is 46.5 years.

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