The age(in years) of 10 teachers in a school are :

34, 37, 53, 46, 52, 43, 31, 36, 40, 50

Find the median age.

By arranging data in ascending order, we get :

31, 34, 36, 37, 40, 43, 46, 50, 52, 53

Number of observations, n = 10, which is even.

By formula,

$\text{Median} = \dfrac{\left(\dfrac{n}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{n}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow\text{Median} = \dfrac{\left(\dfrac{10}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{10}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{5th term} + \text{6th term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{40} + \text{43}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{83}}{2} \\[1em]$

∴ Median = 41.5.

Hence, median is 41.5 years.