Histograms
A histogram is a graphic representation of a variable in the shape of bars (rectangles).
They are used for continuous or discrete variables with a large quantity of data that is grouped into classes.
The base width of the bars (rectangles) are proportional to the class widths and the height is the absolute frequency of each interval.
The surface area of every bar is proportional to the frequency of the represented values.
Frequency Polygon
The frequency polygon is formed by joining the class mark of the intervals by line segments.
Example
The weight of 65 children is given by the following table:
c_{i} | f_{i} | F_{i} | |
---|---|---|---|
[50, 60) | 55 | 8 | 8 |
[60, 70) | 65 | 10 | 18 |
[70, 80) | 75 | 16 | 34 |
[80, 90) | 85 | 14 | 48 |
[90, 100) | 95 | 10 | 58 |
[100, 110) | 105 | 5 | 63 |
[110, 120) | 115 | 2 | 65 |
65 |
Histogram and Polygon of a Cumulative Frequency
If the values from a cumulative frequency table are represented graphically, the result is a cumulative frequency histogram and its corresponding polygon.
Histograms with Different Class Widths
To construct histograms with different class widths, calculate the heights of the rectangles of the histogram.
h_{i} is the height of the interval.
f_{i} is the absolute frequency of the interval.
a_{i} is the class width.
Example
The following table shows the test scores (out of 10) of a group of 50 students.
f_{i} | h_{i} | |
---|---|---|
[0, 5) | 15 | 3 |
[5, 7) | 20 | 10 |
[7, 9) | 12 | 6 |
[9, 10) | 3 | 3 |
50 |