Lecture 3/ Graphic Representation of a Frequency Distribution/2018 -2019 /

Histogram
In drawing the histogram of a given continuous frequency distribution we first mark off along the x-axis all the class intervals on a suitable scale. On each class interval erect rectangles with heights proportional to the frequency of the corresponding class interval so that the area of the rectangle is prortional to the frequency of the class.
If, however, the classes are of unequal width then the height of the rectangle will be proponional to the ratio of the frequencies to the width of the classes.
The diagram of continuous rectangles so obtained is called histrogram.
Remarks
1) To draw the histogram for an ungrouped frequency distribution of a variable we shall have to assume that the frequency corresponding to the variate value x is spread over the interval x-h/2 to x+h/2 , where h the jump from one value to the next.
2. If the grouped frequency distribution is not continuous, first it is to be converted into continuous disiribution and then the histrogam is drawn.
3. Although the height of each rectangle is proportional to the frequency of the corresponding class, the height of a fraction of the rectangle is not proportional to the frequency of the corresponding fraction of the class, so that histogram cannot be directly used to read frequency over a fraction of a class interval.