A histogram is a type of graph that is used in statistics. This kind of graph uses vertical bars to display quantitative data. The heights of the bars indicate the frequencies or relative frequencies of values in our data set.

Although any basic software can construct a histogram, it is important to know what your computer is doing behind the scenes when it produces a histogram. The following walks through the steps that are used to construct a histogram.

With these steps, we could construct a histogram by hand.

### Classes or Bins

Before we draw our histogram, there are some preliminaries that we must do. The initial step involves some basic summary statistics from our data set.

First, we find the highest and lowest data value in the set of data. From these numbers, the range can be computed by subtracting the minimum value from the maximum value. We next use the range to determine the width of our classes. There is no set rule, but as a rough guide, the range should be divided by five for small sets of data and 20 for larger sets. These numbers will give a class width or bin width. We may need to round this number and/or use some common sense.

Once the class width is determined, we choose a class that will include the minimum data value. We then use our class width to produce subsequent classes, stopping when we have produced a class that includes the maximum data value.

### Frequency Tables

Now that we have determined our classes, the next step is to make a table of frequencies. Begin with a column that lists the classes in increasing order. The next column should have a tally for each of the classes. The third column is for the count or frequency of data in each class.

The final column is for the relative frequency of each class. This indicates what proportion of the data is in that particular class.

### Drawing the Histogram

Now that we have organized our data by classes, we are ready to draw our histogram.

- Draw a horizontal line. This will be where we denote our classes.
- Place evenly spaced marks along this line that correspond to the classes.
- Label the marks so that the scale is clear and give a name to the horizontal axis.
- Draw a vertical line just to the left of the lowest class.
- Choose a scale for the vertical axis that will accommodate the class with the highest frequency.
- Label the marks so that the scale is clear and give a name to the vertical axis.
- Construct bars for each class. The height of each bar should correspond to the frequency of the class at the base of the bar. We can also use relative frequencies for the heights of our bars.