Question

The following distribution gives the marks obtained by $102$ students of Class X

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. Of Students	$9$	$10$	$25$	$50$	$5$	$3$

Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.

Answer 1

In this question we will convert the frequency table to a cumulative frequency table and plot the graph and then draw its ogive.

Complete step-by-step solution:
To draw an ogive we require the cumulative frequencies of the values
The distribution table can be written as:

Marks	No. of Students
$0 - 10$	$9$
$10 - 20$	$10$
$20 - 30$	$25$
$30 - 40$	$50$
$40 - 50$	$5$
$50 - 60$	$3$

Now to find the Cumulative frequencies in a less than type cumulative frequency we add all the proceeding terms to the current term, Therefore the cumulative frequency table could be written as:

Marks	No. of Students	Cumulative Frequency
$0 - 10$	$9$	$9$
$10 - 20$	$10$	$9 + 10$
$20 - 30$	$25$	$9 + 10 + 25$
$30 - 40$	$50$	$9 + 10 + 25 + 50$
$40 - 50$	$5$	$9 + 10 + 25 + 50 + 5$
$50 - 60$	$3$	$9 + 10 + 25 + 50 + 5 + 3$

Upon simplifying the above table, we get:

Marks	No. of Students	Cumulative Frequency
$0 - 10$	$9$	$9$
$10 - 20$	$10$	$19$
$20 - 30$	$25$	$44$
$30 - 40$	$50$	$94$
$40 - 50$	$5$	$99$
$50 - 60$	$3$	$102$

Now, we have to plot the graph with taking the upper limit of Marks on X-axis and the respective cumulative frequency on the Y-axis to get the less than ogive.
The points to be plotted to make a less than ogive are on the graph are: ${\text{(10,9), (20,19), (30,44), (40,94), (50,99), (60,102)}}$.

The Curve in the above graph is the Cumulative Frequency Curve i.e. the ogive.

Note: Ogives are useful for determining the median, percentiles, quartiles and five number summaries of data.
The median is simply the value in the middle value when we order the given data.
A quartile is simply a quarter of its own way from the end or the beginning of a given set of ordered data.