Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on. The concept that the area is equal to the probabilities is useful in statistics. The histogram (like the stemplot) can give the shape of the data, the center, and the spread of the data.

Further, the mean, variance, and standard deviation can be calculated and visualized in the probability histogram. The mean is calculated using the equation:

The variance is calculated using the formula:

The standard deviation can be obtained by finding the square root of the variance.

This content is adapted from Openstax, Introductory Statistics, Section 2.2 Histograms