The following table shows the number of patients of different age groups admitted to a hospital for treatment on a day. Find the median of ages of the patients.
| Age- group (Yrs.) | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| No. of patients | 40 | 32 | 35 | 45 | 33 | 15 |
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Solution
| Age (Yrs.) | No. of patients (Frequency) |
Cumulative frequency (Less than) |
| 10-20 | 40 | 40 |
| 20-30 | 32 | 72 |
| 30-40 | 35 | 107 |
| 40-50 | 45 | 152 |
| 50-60 | 33 | 185 |
| 60-70 | 15 | 200 |
Here N = 200 ∴ the number` N/2=`100 which is included in the class 30-40
∴ median class is 30 - 40
∴ L = 30, cf = 72, f = 35, h = 10
Median = L+ `|(n/2-cf)/f| xx h`
`=30+((100-72)/35) xx 10`
`=30+(28xx2)/7`
= 30 + 4 x 2
= 30 + 8 = 38
∴ median of ages of patients is 38.
Concept: Median of Grouped Data
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