# The Marks Obtained by 120 Students in a Test Are Given Below: Draw an Ogive for the Given Distribution on a Graph Sheet. Use a Suitable Scale for Ogive to Estimate the Following: (1) the Median. (2) the Number of Students Who Obtained More than 75% Marks in the Test. (3) the Number of Students Who Did Not Pass the Test If Minimum Marks Required to Pass is 40 - Mathematics

The marks obtained by 120 students in a 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. ofstudents 5 9 16 22 26 18 11 6 4 3

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

Use a suitable scale for ogive to estimate the following:
(1) The median.
(2) The number of students who obtained more than 75% marks in the test.
(3) The number of students who did not pass the test if minimum marks required to pass is 40

#### Solution

 Marks No. of Students Cumulative Frequency 0-10 5 5 10-20 9 14 20-30 16 30 30-40 22 52 40-50 26 78 50-60 18 96 60-70 11 107 70-80 6 113 80-90 4 117 90-100 3 120

n = 120/2 = 60

1) Through marks 60, draw a line segment parallel to x-axis which meets the curve at A. From A, draw a line perpendicular to x-axis meeting at B. Median = 43

2) Through marks 75, draw a line segment parallel to y-axis which meets the curve at D. From D, draw a line perpendicular to y-axis which meets y-axis at 110.

Number of students getting more than 75% = 120 - 110 = 10 students

3) Through marks 40, draw a line segment parallel to y-axis which meets the curve at C. From C, draw a line perpendicular to y-axis which meets y-axis at 52.

The number of students who did not pass = 52.

Concept: Finding the Median, upper quartile, lower quartile from the Ogive
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