Construct an ogive for the following:(vii)
Construct an ogive for the following:(vii)
Marks (more than)$0$$10$$20 $$30$$40$$50$$60$$70$$80$$90$$100$
Cumulative Frequency$100$$87$$65$$55$$42$$36$$31$$21$$18$$7$$0$

Steps to draw a histogram for given frequency distributions,

1. Subtract the frequency of each class with the lower bound of the class interval and from the cumulative frequency to get the cumulative frequency distribution.

2. Then mark the following class limits along the x-axis, taking $1cm=10$ units.

3. Also mark the mark cumulative frequency along the y-axis, taking $1cm=10$ units.

Then,

Marks more thanCumulative Frequency
$0$$100$
$10$$87$
$20$$65$
$30$$55$
$40$$42$
$50$$36$
$60$$31$
$70$$21$
$80$$18$
$90$$7$
$100$$0$

4. So, mark the points (x, f) in the graph, where x is the lower limit of one class and f is the corresponding cumulative frequency, $(0,100)$, $(10,87)$, $(20,65)$, $(30,55)$, $(40,42)$, $(50,36)$, $(60,31)$, $(70,21)$, $(80,18)$, $(90,7)$, $(100,0)$.

5. Finally join the points made by a smooth curve.