Histograms - Displaying Grouped Continuous Data

A histogram looks similar to a bar chart, but it is used for continuous data grouped into intervals called classes. Unlike a bar chart, the bars in a histogram touch each other because the data is continuous – there are no gaps between classes.

The word “histogram” was coined by the influential statistician Karl Pearson in 1891, combining the Greek histos (mast, or something set upright) with gramma (drawing) – a nod to the upright bars standing side by side. Pearson used histograms extensively in his pioneering work on biological measurement and the foundations of modern statistics. Histograms remain essential well beyond the classroom: photo-editing software displays a histogram of an image's pixel brightness so photographers can judge exposure at a glance, and factories use histograms in quality-control processes to check whether a manufactured part's measurements are clustered tightly around the target size or spread dangerously wide.

Histogram vs. Bar Chart

Feature	Bar Chart	Histogram
Data type	Discrete or categorical	Continuous, grouped
Gaps between bars	Yes	No
X-axis	Categories	Numerical scale (class intervals)
Bar width	Equal (and arbitrary)	Equal to class width
What bars show	Frequency	Frequency (or frequency density for unequal classes)

Equal Class Width Histograms

When all classes have the same width, the height of each bar equals the frequency. This is the most common type at introductory level.

Worked Example

Draw a histogram for the following grouped data (class width = 10).

Height (cm)	Frequency
140 – 150	4
150 – 160	9
160 – 170	14
170 – 180	8
180 – 190	5

Total students = 4 + 9 + 14 + 8 + 5 = 40.

The tallest bar is the 160–170 cm class with frequency 14 – this is the modal class.

Key Takeaways

Histograms display grouped, continuous data – bars have no gaps.
The x-axis is a continuous numerical scale, not a list of categories.
When classes have equal width, bar height = frequency.
The class with the tallest bar is called the modal class.

Practice: Grouped Data

Histogram Totals