Question

The monthly profits (in Rs.) of 100 shops are distributed as follows:

Profits per shop:	0-50	50-100	100-50	150-200	200-250	250-300
No. shops:	12	18	27	20	17	6

Draw a histogram for the data and show the frequency polygon for it.

Answer 1

To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the class-intyervals and the frequencies of the class-intervals respectively.

The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with class-intervals as bases and respective frequencies as heights. The scale for horizontal axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 shops.

The heights of the different rectangles are as following

1. The height of the rectangle corresponding to the class-interval 0-50 is big divisions.

2. The height of the rectangle corresponding to the class-interval 50-100 is big divisions.

3. The height of the rectangle corresponding to the class-interval 100-150 is big divisions.

4. The height of the rectangle corresponding to the class-interval 150-200 is big

divisions.

5. The height of the rectangle corresponding to the class-interval 200-250 is big

divisions.

6. The height of the rectangle corresponding to the class-interval 250-300 is big divisions.

The histogram of the given data is as follows:

For frquency polygon, first we will obtain the class marks as given in the following table.

Profits per shop	Class Marks	Number of shops
0-50	25	12
50-100	75	18
100-150	125	27
150-200	175	20
200-250	225	17
250-300	275	6

We plot the points (25, 12), (75, 18), (125, 27), (175, 20), (225, 17) and (275, 6).
Now, we join the plotted points by line segments . The end points (25, 12) and (275, 6) are joined to the mid-points (−25, 0) and (325, 0) respectively of imagined class-intervals to obtain the frequency polygon.

The frequency polygon of the given data is as follows: