Question

40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:

Distance (in m)	12 – 13	13 – 14	14 – 15	15 – 16	16 – 17	17 – 18	18 – 19
No. of students	3	9	12	9	4	2	1

Use a graph paper to draw an ogive for the above distribution.

Use a scale of 2 cm = 1 m on one axis and 2 cm = 5 students on the other axis.

Hence, using your graph, find:

1. the median. 
2. upper quartile.
3. number of students who cover a distance which is above `16 1/2` m.

Answer 1

1. Construct the cumulative frequency table

To draw an ogive (cumulative frequency curve), we first calculate the cumulative frequency for each upper class boundary.

Distance (m)	No. of Students (f)	Cumulative Frequency (cf)	Points to Plot (x, y)
12 – 13	3	3	(13, 3)
13 – 14	9	3 + 9 = 12	(14, 12)
14 – 15	12	12 + 12 = 24	(15, 24)
15 – 16	9	24 + 9 = 33	(16, 33)
16 – 17	4	33 + 4 = 37	(17, 37)
17 – 18	2	37 + 2 = 29	(18, 39)
18 – 19	1	39 + 1 = 40	(19, 40)

2. Draw the Ogive

Using the specified scales (2 cm = 1 m on the x-axis and 2 cm = 5 students on the y-axis), we plot the points and join them with a smooth curve starting from (12, 0).

3. Find the median

The total number of students is N = 40.

The median corresponds to the `N/2`

= `40/2`

= 20^th students.

Locate 20 on the y-axis.

Draw a horizontal line to the curve, then a vertical line down to the x-axis.

Median = 14.67 m (Accepted range: 14.6 – 14.8 m).

4. Find the upper quartile (Q₃)

The upper quartile corresponds to the `(3N)/4`

= `(3 xx 40)/4`

= 30^th student.

Locate 30 on the y-axis.

Draw a horizontal line to the curve, then a vertical line down to the x-axis.

Upper quartile = 15.67 m (Accepted range: 15.6 – 15.8 m).

5. Find students above `16 1/2` m

To find the number of students who covered more than 16.5 m:

Locate 16.5 m on the x-axis.

Draw a vertical line up to the curve, then a horizontal line to the y-axis.

This gives a cumulative frequency of 35 students those who threw ≤ 16.5 m.

Number of students above 16.5 m = Total students – 35

= 40 – 35

= 5 students.

Based on the ogive, the median is approximately 14.67 m, the upper quartile is approximately 15.67 m and there are 5 students who threw a distance above `16 1/2` m.