Question

The marks of 200 students in a test were recorded as follows:

Marks %	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
No. of students	5	7	11	20	40	52	36	15	9	5

Using graph sheet draw ogive for the given data and use it to find the,

1. median,
2. number of students who obtained more than 65% marks
3. number of students who did not pass, if the pass percentage was 35.

Answer 1

Marks (%)	f	cf
0 - 10	5	5
10 - 20	7	12
20 - 30	11	23
30 - 40	20	43
40 - 50	40	83
50 - 60	52	135
60 - 70	36	171
70 - 80	15	186
80 - 90	9	195
90 - 100	5	200

a. Median = `50+ ((100-83)/52xx10)`

`50+(17/52xx10)`

Median = 53.27%

b. 65% lies in the 60–70% class.

From the cumulative frequency table:

Students scoring < 60% = 135

Students scoring < 70% = 171

Approximate number scoring ≤ 65 = `135+(5/10 xx 36)`

= 135 + 18

= 153

⇒ Students scoring > 65 = 200 – 153 = 47 students

c. 35% lies in 30–40% class:

Students scoring < 30% = 23

35 is halfway between 30 and 40:

⇒ Total not passing = 23 + 10 = 33 students