Question

Draw a cumulative frequency curve for the data given below, showing the marks obtained by $64$students in an examination.

Marks	No. of students
$0-10$	$8$
$10-20$	$12$
$20-30$	$20$
$30-40$	$16$
$40-50$	$8$

Answer 1

Step 1: Make the required Cumulative frequency table.

Marks Group	No. of students	Marks	Less than c.f.
$0-10$	$8$	Less than $10$	$8$
$10-20$	$12$	Less than $20$	$20$
$20-30$	$20$	Less than $30$	$40$
$30-40$	$16$	Less than $40$	$56$
$40-50$	$8$	Less than $50$	$64$

Step 2: Construct a Cumulative frequency curve (Ogive) using the following information.

We plot the cumulative frequencies $8,20,40,56,64$ against the upper limits of the corresponding classes$10,20,30,40,50$ respectively.

The smooth curve obtained on joining these points is called the cumulative frequency curve (less than Ogive).