Question

For what value of x is the mode of the data 24, 15, 40, 23, 27, 26, 22, 25, 20, x + 3 found 25? Using this value of x, find the median.

Answer 1

Given: Mode = 25
∴ 25 occurs maximum number of times.

Arranging the given data in ascending order:
15, 20, 22, 23, 24, x + 3, 25, 26, 27, 40

∴ x + 3 = 25
⇒ x = 25 − 3
⇒ x = 22

Hence, the value of x is 22.

Arranging the given data in ascending order:
15, 20, 22, 23, 24, 25, 25, 26, 27, 40

Number of terms = 10 (even)

$$\begin{gathered} \therefore \mathrm{Median}=\mathrm{mean}\mathrm{of}\left[{\left(\frac{n}{2}\right)}^{\mathrm{th}}\mathrm{term}\mathrm{and}{\left(\frac{n}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\mathrm{mean}\mathrm{of}\left[{\left(\frac{10}{2}\right)}^{\mathrm{th}}\mathrm{term}\mathrm{and}{\left(\frac{10}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\mathrm{mean}\mathrm{of}\left[{\left(5\right)}^{\mathrm{th}}\mathrm{term}\mathrm{and}{\left(6\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\mathrm{mean}\mathrm{of}\left[24\mathrm{and}25\right] \\ =\frac{24+25}{2} \\ =\frac{49}{2} \\ =24.5 \end{gathered}$$

Hence, the median is 24.5 .