The table shows the distribution of 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	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 :

(i) The median.

(ii) The inter quartile range.

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

1. The cumulative frequency table for the given continuous distribution is :

2. Take 2 cm along x-axis = 10 scores

3. Take 2 cm along y-axis = 20 (shooters)

4. Plot the points (10, 9), (20, 22), (30, 42), (40, 68), (50, 98), (60, 120), (70, 135), (80, 145), (90, 153) and (100, 160) representing upper class limits and the respective cumulative frequencies.
   Also plot the point representing lower limit of the first class i.e. 0 - 10.

5. Join these points by a freehand drawing.

The required ogive is shown in figure above.

(i) Here, n (no. of students) = 160.

To find the median :

Let A be the point on y-axis representing frequency = $\dfrac{n}{2} = \dfrac{160}{2}$ = 80.

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 point M represents 44.

Hence, the required median score = 44.

(ii) To find lower quartile :

Let B be the point on y-axis representing frequency = $\dfrac{n}{4} = \dfrac{160}{4}$ = 40

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 29.

To find upper quartile :

Let C be the point on y-axis representing frequency = $\dfrac{3n}{4} = \dfrac{480}{4}$ = 120

Through C, draw a horizontal line to meet the ogive at R. Through R, draw a vertical line to meet the x-axis at O. The abscissa of the point O represents 60.

Inter quartile range = Upper quartile - Lower quartile = 60 - 29 = 31.

Hence, the inter quartile range = 31 scores.

(iii) Total marks = 100.

So, more than 85% marks mean more than 85 marks.

Let T be the point on x-axis representing marks = 85.

Through T, draw a vertical line to meet the ogive at S. Through S, draw a horizontal line to meet the y-axis at D. The ordinate of the point D represents 149.

Students who have scored less than 85% = 149.

So, students scoring more than 85% = Total students - Students who have scored less = 160 - 149 = 11.

Hence, there are 11 shooters who obtained a score of more than 85%.