Question

Find the median of the following data:

(iii) $92,35,67,85,72,81,56,51,42,69$

Answer 1

Find the median of the given data.

Given data: $92,35,67,85,72,81,56,51,42,69$

Arrange the observations in ascending order: $35,42,51,56,67,69,72,81,85,92$

Here, the total number of observations $\left(n\right)$ $=10$

When $n$ is even, then median $=\frac{\left({\displaystyle \frac{n}{2}}\right)thvalue+\left({\displaystyle \frac{n}{2}}+1\right)thvalue}{2}$

$$\begin{gathered} =\frac{\left({\displaystyle \frac{10}{2}}\right)thvalue+\left({\displaystyle \frac{10}{2}+1}\right)thvalue}{2} \\ =\frac{\left({\displaystyle 5}\right)thvalue+\left({\displaystyle 5+1}\right)thvalue}{2} \\ =\frac{5thvalue+6thvalue}{2} \\ =\frac{67+69}{2} \\ =\frac{136}{2} \\ =68 \end{gathered}$$

Hence, the median of the given data is $68$.