Histogram and Frequency Distribution:

Histogram is a graphical representation of a frequency distribution. The frequency distribution is a way of organizing data into classes or intervals, along with the corresponding frequencies or counts. The frequency distribution can be of two types:

1. Inclusive type: In this type, the upper limit of one class is the same as the lower limit of the next class. For example, if the classes are 0-9, 10-19, 20-29, and so on, the upper limit of the first class (9) is the same as the lower limit of the second class (10).

2. Exclusive type: In this type, the upper limit of one class is not the same as the lower limit of the next class. For example, if the classes are 0-10, 11-20, 21-30, and so on, the upper limit of the first class (10) is not the same as the lower limit of the second class (11).

Drawing Histogram:

To draw a histogram, we need to follow the steps given below:

1. Choose the appropriate class intervals based on the range of data.

2. Count the number of observations falling within each interval.

3. Draw a horizontal axis (x-axis) representing the class intervals and a vertical axis (y-axis) representing the frequencies.

4. Draw a rectangle for each class interval with the height of the rectangle representing the frequency of that interval. The width of the rectangle should be equal to the width of the class interval.

5. Adjacent rectangles should touch each other, and there should be no gaps between them.

6. Label the x-axis and y-axis appropriately, and give a suitable title to the histogram.

Why Exclusive type of Frequency Distribution is used in Histogram?

Histogram is drawn using the exclusive type of frequency distribution because it ensures that each observation falls into one and only one class interval. This avoids the problem of overlapping intervals that can occur in the inclusive type of frequency distribution.

For example, if a data point falls on the boundary between two intervals in the inclusive type of frequency distribution, it is not clear which interval it belongs to. This can lead to ambiguity and errors in the calculation of frequencies and the drawing of the histogram.

On the other hand, the exclusive type of frequency distribution ensures that each observation belongs to a single interval, and there is no overlap or ambiguity. This makes it easier to calculate frequencies and draw the histogram accurately.

Conclusion:

Thus, we can conclude that the exclusive type of frequency distribution should be used to draw a histogram, as it ensures that each observation belongs to a single interval, and there is no overlap or ambiguity.