Question

The marks obtained by 100 students in a Mathematics test are given below:

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of students	3	7	12	17	23	14	9	6	5	4

Draw an ogive for the given distribution on a graph sheet.

Use a scale of 2 cm = 10 units on both axes.

Use the ogive to estimate the:

1) Median.

2) Lower quartile.

3) A number of students who obtained more than 85% marks in the test.

4) A number of students who did not pass in the test if the pass percentage was 35.

Answer 1

Draw the cumulative frequency table.

Marks	Number of Students (Frequency)	Cumulative Frequency
0-10	3	3
10-20	7	10
20-30	12	22
30-40	17	39
40-50	23	62
50-60	14	76
60-70	9	85
70-80	6	91
80-90	5	96
90-100	4	100

Scale: On x-axis, 1 unit = 10 marks, On y-axis, 1 unit = 10 students

1) Median = `(N/2)^"th" term = (100/2)^"th" term = 50^"th term"`

Draw a horizontal line through mark 50 on the y-axis. The, draw a vertical line from the point it cuts on the graph. The point this line touches the x-axis is the median. Thus, median = 45

2) Lower quartile = `(N/4)^"th" term = (100/4)^"th" term = 25^"th term"`

Draw a horizontal line through mark 25 on the y-axis. The, draw a vertical line from the point it cuts on the graph. The point this line touches the x-axis is the lower quartile

Thus, lower quartile = 31

3) Draw a vertical line through mark 85 on the x-axis. Then, draw a horizontal line from the point it cuts on the graph.

The point where this line touches the y-axis is the number of students who obtained less than 85% marks =93

Thus, number of students who obtained more than 85% marks =100 – 93 = 7

4) Draw a vertical line through mark 35 on the x-axis. The, draw a horizontal line from the point it cuts on the graph.

The point where this line touches the y-axis is the number of students who obtained less than 35% marks = 21