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The Following Table Shows Ages of 3000 Patients Getting Medical Treatment in A Hospital on a Particular Day - Algebra

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Sum

The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day : 

Age (in years) No. of Patients
10-20 60
20-30 42
30-40 55
40-50 70
50-60 53
60-70 20

Find the median age of the patients.

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Solution

Age (in years) No. of Patients c.f.
(less than type)
10-20 60 60
20-30 42 102 → c.f.

30-40

Median class

55 → f 157
40-50 70 227
50-60 53 280
60-70 20 300

Here, N =` 300/2`

N=150

Cumulative frequency just greater than 150 is 157.
∴ Corresponding class (30 – 40) is the median class.
L = 30, f = 55, c.f. = 102, h = 10

`"Median =L"+("N"/2-"c.f")"h"/"f"`

=`30 + (150 - 102) xx(10/55)`

=`30+48 xx (10/55)`

= `30 + 480/55`

=30 + 8.7272

=38.73

Thus, the median age of patients is 38.73 years.

Concept: Median of Grouped Data
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