Question

If the mean of the lower and upper quartile is $10$ and semi-interquartile range is $5$, then the lower quartile and upper quartile respectively are

• A. $2$ and $12$
• B. $3$ and $13$
• C. $4$ and $14$
• D. $5$ and $15$

Answer 1

The correct option is D $5$ and $15$

Let lower quartile and upper quartile be $x$ and $y$, respectively
Mean $=\frac{(x+y)}{2}=10$

So, $x+y=20$ ....(1)

Semi-interquartile range $=\frac{(y-x)}{2}=5$

So, $y-x=10$ ....(2)
Solving the baove 2 equations, we get
$x=5$ and $y=15$