Histograms are frequency distribution plots for a set of continuous data that allow for inspection of underlying distribution, such as normal distribution, outliers, skewness, etc. represented by the population. The data is split into classes, called bins where each bin represents a period containing the number of occurrences in the data set. The area of the bar is indicative of the frequency of occurrences for each bin, which is the product of the height multiplied by the width of the bin. The histogram is then constructed by tabulating the frequencies in each bin and plotting them against the intervals. There is no formula to determine the ideal bin size, but one must make sure that the bins are neither too small nor too large, in which case the underlying pattern of frequency distribution becomes elusive. Histograms represent continuous data sets and hence, do not have “gaps” between the bars, although bars might be absent reflecting no frequencies.

A histogram displays numerical or categorical data. These are useful to not only convey a large amount of information faster in the form of charts, but also estimate a variable’s mean, standard deviation, skewness, and kurtosis, all of which describe the underlying distribution. Histograms can answer questions like determining whether the outputs of two or more processes are distributed normally or if they are different, whether a process has changed over time intervals and if so, how the shapes of the distributions may vary, and analyzing whether processes can meet specific requirements.

There are several types of distributions found within histograms. A normal distribution is symmetric with the mean being at the center and the likelihood of points occurring on either side of the average being equal. Similarly, a bimodal distribution has two peaks instead of one and the data is analyzed as separate normal distributions. There is the right skewed and left skewed distribution where a large number of data values occur on the right or left side, respectively. Lastly, a random distribution is one that lacks a pattern and usually exhibits multiple peaks, in which case the data should be analyzed separately.