Question

The table shows the distribution of the scores obtained by $160$ shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution.

Scores	No. of shooters
$0-10$	$9$
$10-20$	$13$
$20-30$	$20$
$30-40$	$26$
$40-50$	$30$
$50-60$	$22$
$60-70$	$15$
$70-80$	$10$
$80-90$	$8$
$90-100$	$7$

Use your graph to estimate the following the interquartile range

Answer 1

Scores	No. of shooters	c.f.
$0-10$	$9$	$9$
$10-20$	$13$	$22$
$20-30$	$20$	$42$
$30-40$	$26$	$68$
$40-50$	$30$	$98$
$50-60$	$22$	$120$
$60-70$	$15$	$135$
$70-80$	$10$	$145$
$80-90$	$8$	$153$
$90-100$	$7$	$160$

Lower quartile $Q_1={\left(\frac{n}{4}\right)}^{th}term$
$={\left(\frac{3\times 160}{4}\right)}^{th}term={40}^{th}term$
$=28.5$
Upper quartile $Q_3={\left(\frac{3n}{4}\right)}^{th}term$
$={\left(\frac{3\times 160}{4}\right)}^{th}term={120}^{th}term$
$=60$
Inter quartile range $=Q_3-Q_1$
$=60-28.5=31.5$