The following table shows ages of 300 patients getting medical treatment in a hospital on a particular day. Find median age of a patient.
| Age (in years) | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
|---|---|---|---|---|---|---|
| No. of patients | 60 | 42 | 55 | 70 | 53 | 20 |
Solution:
Classes
(Age in years)Frequency ($f_i$)
(No. of patients)Cumulative frequency
less than type10 - 20 60 60 20 - 30 42 102 $\rightarrow c.f.$ 30 - 40 55 $\rightarrow f$ 157 40 - 50 70 227 50 - 60 53 280 60 - 70 20 300 Total 300 $\rightarrow \text{N}$ Here total frequency = $\Sigma f_i = \text{N} = 300$
$\frac{\text{N}}{2} = \frac{300}{2} = 150$
Cumulative frequency (less than type) which is just greater than 150 is 157. Therefore corresponding class 30 - 40 is median class.
$L = 30$, $\text{N} = 300$, $c.f. = 102$, $f = 55$, $h = 10$
$$\begin{align*} \text{Median} &= L + \left( \frac{\text{N}}{2} - c.f. \right) \frac{h}{f} \\ &= 30 + \left( \frac{300}{2} - 102 \right) \frac{10}{55} \\ &= 30 + (150 - 102) \frac{10}{55} \\ &= 30 + (48) \frac{10}{55} \\ &= 30 + (48) \frac{2}{11} \\ &= 30 + \frac{96}{11} \\ &= 30 + 8.73 \\ &= 38.73 \end{align*}$$Median of age is 38.73 years.