Question

Draw a frequency curve for the data on marks obtained by 74 students in an examination given in the table below:

Marks:	0-10	10-20	20-30	30-40	40-50
No. of Students:	8	32	18	10	6

Answer 1

Hint:
Here, we will draw a frequency curve for the given data. A frequency curve is a curve that represents the frequencies of the distribution graphically. It can be drawn by using the histogram. The total area of a frequency curve is unity.

Complete Step by Step Solution:
We know that the frequency curve is a smooth curve which can be drawn by joining the midpoints of the histogram.
We will plot marks on the $$x$$ axis and the number of students on the $$y$$ axis.
We will use the following process to draw the frequency curve:
1) We will plot the histogram for the data values.
2) Then, we will point the midpoints of the class interval on the histogram.
3) Now we will join the midpoints using the straight lines.
4) The graph joined by using straight lines is called frequency polygon.
The frequency polygon for the data is as follows:

Now, we will be joining the midpoints of the histogram using curves.
The graph joined by using the curve is called frequency curve.
Therefore, the frequency curve for the given data as follows:

Note:
We know that frequency curve is a limiting form of either histogram or frequency polygon. We have four types of frequency curves which include bell shaped curve, U- shaped curve, J-shaped curve and mixed curve. Since the frequency for the data values start from the minimum value 8, then reaches its maximum point 32 and then gradually decreases at the final point 6. Thus, the curve obtained is a bell shaped curve. Usually if the data values are marks or profit, then the frequency curve would be a bell shaped curve.