Question

The runs scored by a batsman in seven innings are $28,60,85,58,74,20,90$. Find $Q_1,Q_2,Q_3$ and quartile deviation

Answer 1

Arranging the scores in ascending we get,
$20,28,58,60,74,85,90$.
There are $7$ scores and $n=7$.
i) First quartile $\left(Q_1\right)=\frac{n+1}{4}thscore=\frac{7+1}{4}thscore=2^{nd}score=28$.
ii) Median $\left(Q_2\right)=\frac{n+1}{2}thscore=\frac{7+1}{2}thscore=4^{th}score=60$.
(iii) Third quartile $\left(Q_3\right)=\frac{3(n+1)}{4}=\frac{3(7+1)}{4}thscore=6^{th}score=85$.
(iv) Quartile deviation $=\frac{Q_3-Q_1}{2}=\frac{85-28}{2}=28.5\approx 29$.