Question

Find the median of the data
46, 41, 77, 58, 35, 64, 87, 92, 33, 55, 90.
In the above data, if 41 and 55 are replaced by 61 and 75 respectively, what will be the new median?

Answer 1

Arranging the given data in ascending order:
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

Number of terms = 11 (odd)

$$\begin{gathered} \therefore \mathrm{Median}={\left(\frac{n+1}{2}\right)}^{\mathrm{th}}\mathrm{term} \\ ={\left(\frac{11+1}{2}\right)}^{\mathrm{th}}\mathrm{term} \\ =6^{\mathrm{th}}\mathrm{term} \\ =58 \end{gathered}$$

Hence, the median of the data is 58.

Now, In the above data, if 41 and 55 are replaced by 61 and 75 respectively.
Then, new data in ascending order is:
33, 35, 46, 58, 61, 64, 75, 77, 87, 90, 92

Number of terms = 11 (odd)

$$\begin{gathered} \therefore \mathrm{Median}={\left(\frac{n+1}{2}\right)}^{\mathrm{th}}\mathrm{term} \\ ={\left(\frac{11+1}{2}\right)}^{\mathrm{th}}\mathrm{term} \\ =6^{\mathrm{th}}\mathrm{term} \\ =64 \end{gathered}$$

Hence, the new median of the data is 64.