Question

Draw and give the cumulative frequency polygon for the following frequency distribution by less than method.

Marks:	0-10	10-20	20-30	30-40	40-50	50-60
Number of students:	7	10	23	51	6	3

Answer 1

Given are the marks of students.

For constructing a less than cumulative frequency polygon, we will prepare the cumulative frequency table for the given data, as shown below:

$\text{Marks}$	$\text{Number of Students}$	$\text{Marks Less Than}$	$\text{Cumulative Frequency}$
$0-10$	$7$	$10$	$7$
$10-20$	$10$	$20$	$17$
$20-30$	$23$	$30$	$40$
$30-40$	$51$	$40$	$91$
$40-50$	$6$	$50$	$97$
$50-60$	$3$	$60$	$100$

For starting the graph, we will assume that there is an interval $-10-0$ having $0$ frequency.

For constructing the less than cumulative frequency polygon, we will plot the upper class limits along with their corresponding cumulative frequency value on the graph, taking suitable scale. We will take the marks on x-axis and the cumulative frequency on the y-axis.

The points to be plotted are $(10,7),(20,17),(30,40),(40,91),(50,97)and(60,100)$.

Once, we join this points, we will get the required less than cumulative frequency polygon, as shown in the graph given above.