6.4 : Probability Histograms

Probability histograms provide visual insights into the centering and spread of probability distributions that are difficult to comprehend in tabular form.

Consider a case of the number of seats occupied in a carpool. 

Based on daily observation, the probability that any number of seats between one to five is occupied is calculated. Here, the occupied seat count is the random variable.

Plotting a histogram with the number of seats occupied on the X-axis and corresponding probabilities on the Y-axis creates a probability histogram.

Each of these rectangular bars is one unit wide. This means that the area of each rectangle also represents the probability of each outcome.

To get more insights into the data, mean and variance can be calculated using the distribution table. 

To find the mean, multiply x with the corresponding probability, and add them up. 

Similarly, multiply the square of the x minus population mean by the probability, and add them up to obtain the variance.

The square root of the variance gives the standard deviation.