Question

The median of the observations $11,12,14,(x-2),(x+4),(x+9),32,38,47$ arranged in ascending order is $24$. Find the value of $x$ and hence find the mean.

• A. $x=20$, Mean $=25$
• B. $x=20$, Mean $=24$
• C. $x=15$, Mean $=25$
• D. $x=18$, Mean $=20$

Answer 1

Answer: (A)

$x=20$, Mean $=25$

Median = 24

No. of observation = 9

Median = ${\frac{\left(n+1\right)}{2}}^{th}\text{observation}$

$={\left(\frac{9+1}{2}\right)}^{th}=5^{th}$

$=x+4$

Median = x + 4

24 = x + 4

x= 20

Mean = $\frac{\text{sum of observation}}{\text{No}\text{. of observation}}$

$\text{=}\frac{\text{225}}{\text{9}}=25$