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. (Take 2 cm = 10 scores on the X-axis and 2 cm = 20 shooters on the Y-axis).

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

Use your graph to estimate the following:

1) The median

2) The interquartile range.

3) The number of shooters who obtained a score of more than 85%.

Answer 1

Scores	f	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
	n = 160

1) Median = `(n/2)^"th" term  = (160/2)^"th"` term =80 term.

Through mark 80 on the y-axis, draw a horizontal line which meets the ogive drawn at point Q.

Through Q, draw a vertical line which meets the x-axis at the mark of 43.

⇒ Median = 43

2) Since the number of terms = 160

Lower quartile `(Q_1) = (160/4)^"th" "term" 120^"th" " term" = 60`

∴ Inter-quartile range = `Q_3 - Q_1` = 60 - 28 = 32

3) Since 85% scores = 85% of 100 = 85

Through mark for 85 on x-axis, draw a vertical line which meets the ogive drawn at point B.

Through the point B, draw a horizontal line which meets the y-axis at the mark of 150.

⇒ Number of shooters who obtained more than 85% score=160-150=10