Often in statistics, it’s good to represent the data in the form of a graph. One type of graph used is a histogram, which provides data visually organized into frequency tables. In a histogram, bars are used to represent each class. The width of the bar determines the class width and the height of the bar determines the class frequency. How is a histogram made and what types of distributions may be displayed through a histogram?
To make a histogram, first create a frequency table with designated number of classes. For example, suppose you wish to create a histogram for commute distances of 100 workers in Philadelphia, Pennsylvania. Suppose the distances are between 1 and 54 miles. We can select 6 classes, each of width 9. The first class is then 1-9, second 10-18, third 19-27, and so on. Suppose the frequencies range from 1 to 20. Place the class boundaries on the horizontal axis and the frequencies on the vertical axis. Now, draw a bar with that is the width of the class boundary and the height of the class frequency. For example, if there are 10 people who commute 1 to 9 miles to work, the height of the bar is 10 and the width goes from 1 to 9 on the horizontal axis.
There are several types of histograms with terms used to describe their appearance. They are as follows:
This describes a distribution that is the same, or nearly the same, on both sides. To make this even more clear, imagine folding the graph down the middle vertically. When doing so a symmetrical distribution will be the same on both sides of the fold. The most common symmetrical distribution is the normal distribution, which is the class bell-shaped curve.
This type of distribution has a histogram which every class has the same frequency. The uniform distribution is also symmetrical, but has the distinguishing characteristic that each bar is of equal height. It’s also called “rectangular” because the shape of the histogram is a rectangle.
This type of distribution has a histogram where one tail is longer than the other. The distribution is said to be skewed right if the tail is elongated to the right. Likewise, the distribution is said to be skewed left if the tail is elongated to the left.
This type of distribution has a histogram that have two peaks separated by one or more classes. The heights of the two highest frequencies may differ slightly or be the same. For example, suppose the class from 10 – 18 miles and the class from 37 – 45 have the highest frequencies of 10 and 12, respectively. Since these are close to being the same frequency and they are separated by one or more classes, then the distribution is bimodal.
This guide should help those with confusion about what a histogram is, how to construct a histogram, and what population distributions are represented by a histogram.