Question

Find the median of the following data (1-8)
92, 35, 67, 85, 72, 81, 56, 51, 42, 69

Answer 1

Arranging the given data in ascending order, we have:

35, 42, 51, 56, 67, 69, 72, 81, 85, 92

Here, n = 10, which is even.

$$\begin{gathered} \mathrm{Median}=\frac{\mathrm{Value}\mathrm{of}{\left({\displaystyle \frac{n}{2}}\right)}^{\mathrm{th}}\mathrm{observation}+\mathrm{Value}\mathrm{of}{\left({\displaystyle \frac{n}{2}+1}\right)}^{\mathrm{th}}\mathrm{observation}}{2} \\ \Rightarrow \mathrm{Median}=\frac{\mathrm{Value}\mathrm{of}{\left({\displaystyle 5}\right)}^{\mathrm{th}}\mathrm{observation}+\mathrm{Value}\mathrm{of}{\left({\displaystyle 6}\right)}^{\mathrm{th}}\mathrm{observation}}{2} \\ \Rightarrow \mathrm{Median}=\frac{67+69}{2}=\frac{136}{2} \\ \Rightarrow \mathrm{Median}=68. \end{gathered}$$
Hence, the median of the given data is 68.