2.8: Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).

A histogram graph consists of contiguous (adjoining) boxes. The heights of the bars correspond to frequency values. The graph will have the same shape with respective labels. The histogram (like the stemplot) can give the shape, the center, and the spread of the data. One will typically use a histogram to display large, continuous, quantitative data sets. The main advantage of a histogram is that it can readily display large data sets. A rule of thumb is to use a histogram when the data set consists of 100 values or more. To construct a histogram, one can decide how many bars or intervals, also called classes, represent the data. Many histograms consist of five to 15 bars or classes for clarity, yet one can choose the number of bars that are needed.

Recall that frequency distribution tables help  organize quantitative data with several categories, such as the number of books at different price ranges.

Such frequency distribution tables can be visually represented using histograms, a graph that consists of bars of equal width drawn without gaps. 

The vertical axis represents the frequencies in each class, and the horizontal axis represents the class boundaries. 

So, what are class boundaries? The first interval in the data table shows the price ranging from 5 to 10 dollars, and the second interval offers  the price range from 11 to 16. 

Note that the price range between 10 and 11 is missing from the table. This gap is filled in by calculating their midpoints, called the class boundaries.

These class boundaries are represented on the horizontal axis and the corresponding frequencies on the vertical axis. The vertical bars, called bins, connect the class boundaries and frequency values.