The table below shows the distribution of the scores obtained by 120 shooters in shooting competition. Using a graph sheet, draw an ogive for the distribution.

Scores obtained	Number of shooters
0 - 10	5
10 - 20	9
20 - 30	16
30 - 40	22
40 - 50	26
50 - 60	18
60 - 70	11
70 - 80	6
80 - 90	4
90 - 100	3

Use your ogive to estimate :

(i) the median

(ii) the inter-quartile range

(iii) the number of shooters who obtained more than 75% score.

Cumulative frequency distribution table :

Here, n = 120, which is even.

(i) Steps of construction:

1. Take 1 cm along x-axis = 10 scores

2. Take 2 cm along y-axis = 20 shooters

3. Plot the point (0, 0) as ogive starts from x- axis representing lower limit of first class.

4. Plot the points (10, 5), (20, 14), (30, 30), (40, 52), (50, 78), (60, 96), (70, 107), (80, 113), (90, 117), (100, 120)

5. Joint the points by a free hand curve.

To find the median :

Let A be the point on y-axis representing frequency = $\dfrac{\text{n}}{2} = \dfrac{120}{2}$ = 60.

Through A draw a horizontal line to meet the ogive at P. Through P, draw a vertical line to meet the x-axis at M. The abscissa of the points M represents 43.

Hence, the median is 43.

(ii) To find lower quartile:

Let B be the point on y-axis representing frequency = $\dfrac{\text{n}}{4} = \dfrac{120}{4}$ = 30.

Through B, draw a horizontal line to meet the ogive at Q. Through Q, draw a vertical line to meet the x-axis at N. The abscissa of the point N represents 30.

To find upper quartile:

Let C be the point on y-axis representing frequency = $\dfrac{3\text{n}}{4} = \dfrac{3 \times 120}{4} = \dfrac{360}{4}$ = 90.

Through C, draw a horizontal line to meet the ogive at R. Through R, draw a vertical line to meet the x-axis at S. The abscissa of the point S represents 56.

Inter-quartile range = Upper quartile - Lower quartile = 56 - 30 = 26

Hence, the inter quartile range is = 26.

(iii) Total score = 100

So, more than 75% score mean more than 75 score.

Let T be the point on x-axis representing scores = 75

Through T, draw a vertical line to meet the ogive at G. Through G, draw a horizontal line to meet the y-axis at D. The ordinate of the point D represents 110

Shooters who have scored less than 75% = 110

So, students scoring more than 75% = Total students - Students who have scored less = 120 - 110 = 10

Hence, there are 10 number of shooters who obtained more than 75% score.