Histogram

A histogram graphically represents a variable using bars (rectangles).

The surface area of every bar is proportional to the frequency of the represented values.

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.

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:

  ci fi Fi
[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


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.

Histogram and Polygon of a Cumulative Frequency


Histograms with Different Class Widths

To graph histograms with different class widths, calculate the heights of the rectangles of the histogram.

Histogram with Different Class Widths Formula

hi is the height of the interval.

fi is the absolute frequency of the interval.

ai is the class width.

Example

The following table shows the test scores (out of 10) of a group of 50 students.

  fi hi
[0, 5) 15 3
[5, 7) 20 10
[7, 9) 12 6
[9, 10) 3 3
  50  

Histogram with Different Class Widths





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