ICSE Class X Math 2016 Paper

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.
(Take $2\,\mathrm{cm}=10$ scores on the $X$ axis and 2 $c\,m=20$ shooters on the $Y$ -axis).

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 :

Question : 31 of 57

Marks: +1, -0

The interquartile range. .

Solution:

Lower quartile

Q_1 = \left( \frac{n}{4} \right)^{\text{th }} \text{ term }

= \left( \frac{160}{4} \right)^{\text{th }} \text{ term }

= 40^{\text{th }} \text{ term } = 28.5

Upper quartile

Q_3 = \left( \frac{3n}{4} \right)^{\text{th }} \text{ term }

= \left( \frac{3 \times 160}{4} \right)^{\text{th }} \text{ term }

= 120^{\text{th }} \text{ term } = 60

Inter quartile range

= Q_3 - Q_1

= 60 - 28.5 = 31.5

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