As a teacher of junior maths and Maths in Society, I used to think that a histogram was a rather trivial statistical object, sort of a bar graph with the gaps removed to save space. A modern data-centred approach to statistics starts with viewing the data in a variety of ways. Features of interest to a statistician are the overall shape of the data, symmetry, the location and the spread, existence of outliers and evidence of clusters or gaps. A histogram with a scale on the horizontal axis is generally useful for showing all of these features, though for some distributions the features of a dataset can be disguised or distorted due to a particular choice of bin width. One application of the humble histogram is determining if a set of data is approximately normally distributed, though a histogram is most effective with for this purpose if the dataset is large.
Normality is a pre-condition for certain analyses of data, including many hypothesis tests.
While there are formal tests of normality, often a quick look at a histogram of the data is sufficient. And no statistican would rely strictly on formal tests without viewing the data also. Compared A histogram shows much the same information as a stemplot, though for a given dataset one or the other of these methods of displaying the data may be preferable. Students will improve their ability to visualise the shape of a distribution given the summary statistics . Bin Width Statistics computer programs and graphical calculators will generate a default histogram if bin width or the number of bins is not specified.