Question

The marks scored by $6$ students in a preparatory exam are given here:
$56,71,49,90,75.88$.
Find the median score and semi-quartile range

Answer 1

Arranging the scores in ascending order we get,
$49,56,71,75,88,90$.
$Median=\frac{6+1}{2}thscore=3.5thscore$
$=3^{rd}score+0.5(4^{th}score-3^{rd}score)$
$Median=71+0.5(75-71)=71+2=73marks$.
To find semi-inter quartile range
$Q_1=\frac{6+1}{2}thscore={1.7}^{th}score$
$=1stscore+0.75(2^{nd}score-1^{st}score)$
$Q_1=49+0.75(56-59)=49+0.75\left(7\right)=49+5.25=54.25\approx 54marks$.
$Q_3=\frac{3(6+1)}{4}thscore={5.25}^{th}score$
$=5^{th}score+0.25(6^{th}score-5^{th}score)$
$Q_3=88+0.25(90-88)=88+0.5=88.5\approx 89$.
Hence
semi-inter quartile range $=\frac{Q_3-Q_1}{2}=\frac{89-54}{2}=\frac{35}{2}=17.6\approx 18$.