# For what value of x is the mode of the data 24, 15, 40, 23, 27, 26, 22, 25, 20, x + 3 found 25?

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.

Solution:

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)

$\therefore$ Median $=$ mean of $\left[\left(\frac{n}{2}\right)^{\text {th }}\right.$ term and $\left(\frac{n}{2}+1\right)^{\text {th }}$ term $]$

$=$ mean of $\left[\left(\frac{10}{2}\right)^{\text {th }}\right.$ term and $\left(\frac{10}{2}+1\right)^{\text {th }}$ term $]$

$=$ mean of $\left[(5)^{\text {th }}\right.$ term and $(6)^{\text {th }}$ term $]$

$=$ mean of $[24$ and 25$]$

$=\frac{24+25}{2}$

$=\frac{49}{2}$

$=24.5$

Hence, the median is 24.5 .