Probability Histogram vs Histogram
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Probability histogram
Random variables and distributions
A probability histogram is a bar graph of a discrete probability distribution in which each bar's height is the probability of that value.
A probability histogram looks like a histogram of data, except the bar heights are probabilities instead of counts, so the heights add to 1. Rolling a fair die gives six bars of equal height , and . The mean of the random variable is the balance point of the picture, which for the die is (mu-X, the mean of X). You read shape from it the same way you read shape from data: look for symmetry, skew, and gaps.
Histogram
Graphs and displays
A histogram displays quantitative data by grouping values into equal-width intervals and drawing a bar for the count in each interval.
A histogram divides the number line into bins of equal width and draws a bar whose height is the frequency in that bin. For example, exam scores might be binned as 60 to 70, 70 to 80, and 80 to 90, with bar heights giving how many scores land in each. Unlike a bar graph, the bars touch because the horizontal axis is a continuous number scale. The bin width you choose affects how smooth or jagged the shape looks.