Question

The mean of 1, 7, 5, 3, 4, and 4 is m. The observations 3, 2, 4, 2, 3, 3 and p have mean (m - 1) and median q. Find p q.

• A. p = 1, q = 2
• B. p = 4, q = 2
• C. p = 3, q = 3
• D. p = 4, q = 3

Answer 1

The correct option is D p = 4, q = 3

Mean $=\frac{1+7+5-3+4+4}{6}\Rightarrow m=\frac{24}{6}=4$
Also, $m-1=\frac{3+2+4+2+3+3+p}{7}$
$\Rightarrow 21=17+p$
$\Rightarrow p=4$
First we arrange the observations in ascending order. i.e. 2, 2, 3, 3, 4, 4.
Since, no. of observations is odd
$\therefore$ Median $={\left(\frac{7+1}{2}\right)}^{th}$ observation
$q=4^{th}$ observation.
q = 3