Question

Observations of some data are $\frac{x}{5},x,\frac{x}{3},\frac{2x}{3},\frac{x}{4},\frac{2x}{5}$ and $\frac{3x}{4}$ where $x>0$. If the median of the data is $4$, then find the value of $x$.

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is D $10$

Median is the middle value of the data values after arranging the data values in the ascending or descending order.

If $n$ is odd, then the median is $(\frac{n+1}{2}{)}^{th}$ value.

If $n$ is even, then the median is ${\frac{(\frac{n}{2}{)}^{th}+(\frac{n}{2}+1)}{2}}^{th}$ value.

Given data values are $\frac{x}{5},x,\frac{x}{3},\frac{2x}{3},\frac{x}{4},\frac{2x}{5},\frac{3x}{4}$

Arranging the data values in the ascending order we get $\frac{x}{5},\frac{x}{4},\frac{x}{3},\frac{2x}{5},\frac{2x}{3},\frac{3x}{4},x$

Given that median of the data is $4$

Total number of values is $n=7$ (odd)

Therefore, the median is $(\frac{7+1}{2}{)}^{th}$ value = $4^{th}$ value = $\frac{2x}{5}$

$⟹4=\frac{2x}{5}$

$⟹2x=20⟹x=10$