Histogram

Histogram

 In drawing the histogram of a given continuous frequency

distribution we first mark off along the x-axis all the class interval~ 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

proportional to the frequency of the class. If . However , the classes are of unequal

width then die height of the rectangle will be proportional to the ratio of the

frequencies to the width of the classes. 7be diagram of continuous rectangle so

obtained is called histogram.

Remarks

1. To draw the histogram for an ungrouped frequency distribution

of a variable we shall have to assume that the frequency corresponding

value x is spread. over the interval x - hl2 to x + hl2, where h is 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 distribution and then the histogram 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.

4. The histogram of the distribution of marks of250 students in Table 3 (page

2·2) is obtained as follows.

Since the grouped frequency distribution is not continuous, we first convert it

into a continuous distribution as follows