Histogram
A histogram is a type of graph that uses adjacent bars to show how often data values fall within certain intervals. Unlike a regular bar chart, the bars touch each other because the data is continuous and grouped into ranges.
A histogram displays the frequency distribution of a numerical dataset by dividing the data into equal-width intervals called bins or classes. Each bar's height represents the frequency (or relative frequency) of data values within that interval. The bars are drawn adjacent to one another, reflecting the continuous nature of the underlying data. The horizontal axis shows the intervals and the vertical axis shows frequency.
Example
Problem: 20 students took a test. Their scores were: 52, 55, 61, 63, 65, 67, 70, 72, 73, 75, 76, 78, 80, 81, 83, 85, 88, 91, 94, 97. Draw a histogram using intervals of width 10, starting at 50.
Step 1: Set up your intervals (bins). Starting at 50 with width 10 gives: 50–59, 60–69, 70–79, 80–89, 90–99.
Step 2: Count how many scores fall in each interval.
Step 3: Draw a horizontal axis labelled 'Score' with the interval boundaries marked: 50, 60, 70, 80, 90, 100.
Step 4: Draw a vertical axis labelled 'Frequency' scaled from 0 to at least 6. For each interval, draw a bar reaching the correct frequency. The bars must touch — there are no gaps between them.
Answer: The completed histogram has five touching bars with heights 2, 4, 6, 5, and 3. The tallest bar (70–79) shows that most students scored in that range.
Visualization
Why It Matters
Histograms appear throughout science, economics, and everyday data analysis whenever you need to see how values are spread across a range — for example, visualising exam score distributions, age groups in a population, or rainfall amounts by month. Recognising the shape of a histogram (symmetric, skewed, or bimodal) tells you a lot about the data before doing any calculations.
Common Mistakes
Mistake: Leaving gaps between the bars, treating the histogram like a bar chart for categorical data.
Correction: Histograms show continuous numerical data grouped into intervals, so the bars must touch. Gaps would incorrectly suggest there are no values between the intervals.
Mistake: Using unequal interval widths without adjusting bar heights to show frequency density.
Correction: When all intervals are equal width, bar height can represent frequency. If interval widths differ, you must use frequency density (frequency ÷ class width) on the vertical axis, otherwise wider bars will look misleadingly large.