Question

Draw less than ogive for the following data.

Marks	Frequency	Cumulative Frequency
0-10	2	2
10-20	8	10
20-30	12	22
30-40	18	40
40-50	28	68
50-60	22	90
60-70	6	96
70-80	4	100

Answer 1

Hint: To draw less than ogive for the given data, we have drawn X and Y axes. We will take cumulative frequencies along the y-axis and the upper-class limits on the x-axis. Now, we should plot cumulative frequencies against each upper class. We have drawn a continuous curve by connecting these points.

Complete step-by-step answer:
We have to draw less than ogive for the given data. Let us see what an ogive is.
Ogive displays the frequency distribution graph of a series. It is a graph of a cumulative distribution, which explains data values on the horizontal plane axis and either the cumulative relative frequencies, the cumulative frequencies or cumulative percent frequencies on the vertical axis.
Ogive graphs are frequency graphs that are used to exhibit the characteristics of discrete and continuous data. There are two types of ogive –Less than and More than.
Here, we have to plot less than ogive. Let us see the steps to do this.
Step1: We have to draw X and Y axes.
Step2: We will take cumulative frequencies along the y-axis and the upper-class limits on the x-axis.
Step3: Now, we should plot cumulative frequencies against each upper class.
Step4: We have to draw a continuous curve by connecting these points.
We have the data:

Marks	Frequency	Cumulative Frequency
0-10	2	2
10-20	8	10
20-30	12	22
30-40	18	40
40-50	28	68
50-60	22	90
60-70	6	96
70-80	4	100

The less than ogive curve will be as follows:

Note: We should plot the upper class limits not the lower class limits. If we plot lower class limits it would be a greater than or more than ogive. We should plot cumulative frequency not frequency. Do not plot cumulative frequency on X-axis and upper limit on Y-axis.