Frequency and Histograms

A step-by-step guide to frequency and histograms

A histogram is a graphical representation of data in which the data is grouped into continuous numerical ranges, with each range corresponding to a vertical bar. For education statistics and research, visit the National Center for Education Statistics.

• The horizontal axis shows the range of numbers.
• The vertical axis (frequency) represents the amount of data in each range.

The range of numbers depends on the data used.

Parts of a histogram:

• Title: The title describes the information in the histogram.
• \(x\)-Axis: The \(x\)-axis is the interval that represents the scale of values that the measurements fall under.
• \(y\)-Axis: The \(y\)-axis shows the number of times the values occurred in the intervals specified by the \(x\)-axis.
• Bars: The height of the bar indicates the number of times the values occurred in the interval, while the width of the bar indicates the interval covered. The width should be the same across all bars for a histogram with equal bins.

How to plot a histogram?

To make a histogram, you must follow the steps below:

1. Start by marking class intervals on the \(x\)-axis and frequencies on the \(y\)-axis.
2. The scale must be the same for both axes.
3. Class intervals must be exclusive.
4. Draw rectangles with bases as class intervals and corresponding frequencies as heights.
5. A rectangle is drawn over each class interval as class limits are shown on the horizontal axis and frequencies are shown on the vertical axis.
6. The height of each rectangle is proportional to the frequency of the corresponding class if the intervals are equal.
7. If the intervals are unequal, the area of each rectangle is proportional to the corresponding class frequency.

Frequency histogram

A frequency histogram is a histogram that shows the frequency (number of occurrences) of given items.