Histograms and Frequency Density

Histograms are a tool for visualising frequency distributions, particularly those involving continuous data. They use horizontal bars to represent the frequency density of numerical data.
The horizontal axis (x-axis) of a histogram categorises the data into intervals or bins, while the vertical axis (y-axis) shows the frequency density. Each bar spans an interval along the x-axis and its height corresponds to the frequency density of that interval.
Frequency density is calculated by dividing the frequency of each data interval by its class width. This means that the area of each bar in a histogram is proportional to the frequency of the data it represents.
The class width is the difference between the upper and lower boundaries of a bin, also known as a class interval. Counts and other discrete data use fixed class intervals.
Histograms can be used to identify patterns, like symmetric or skewed distributions, repetition (or periodicity), and outliers. They also provide a visual representation for median, mode, and range.
If the data is skewed left, most of the data points fall into the right of the histogram. If the data is skewed right, most data points fall to the left.
In histograms, gaps between bars represent gaps in the data or absence of observations in the class intervals. Overlapping bars do not exist in histograms, as all pieces of data belong to one class interval only.
To create a histogram, first organise your data into class intervals and tally the frequency of observations in each. Then calculate the frequency density for each interval. Finally, mark your class intervals on the x-axis and the frequency densities on the y-axis, then draw your bars.
Be aware of potential misinterpretations: A taller bar does not always mean more data in that group because the height of the bar represents the frequency density, not frequency. Remember, the actual frequency is obtained by multiplying the frequency density by the class width. Be careful in interpretations.
Use histograms in combination with other statistical tools, like the box plot, for an efficient and comprehensive data analysis. Every data visualisation tool has a unique strength that can reveal parts of your data’s story.