ICSE Class X Math 2016 Solved 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 $2 {\cm}=10$ 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\;= (\;{n}/{4}) ^{\;\text "th "\;} \;\text " term "\;

\;= (\;{160}/{4}) ^{\;\text "th "\;} \;\text " term "\;

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

Upper quartile

Q_3\;= (\;{3 n}/{4}) ^{\;\text "th "\;} \;\text " term "\;

\;= (\;{3 × 160}/{4}) ^{\;\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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