Histogram Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Histogram.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

A histogram is a graph that groups numerical data into equal-width ranges (bins) and shows the frequency of values in each range using adjacent bars that touch. Unlike bar graphs, histograms display the distribution shape of continuous data.

Unlike bar graphs for categories (red, blue, green), histograms are for numbers grouped into ranges. Test scores 60-70, 70-80, 80-90... The bars touch because the data is continuous - there's no gap between 69.9 and 70.0.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A histogram shows the distribution of numerical data by grouping values into equal-width bins. The bars touch because the underlying data is continuous.

Common stuck point: Students confuse histograms with bar graphs — histograms have no gaps between bars and use numerical ranges, not named categories.

Sense of Study hint: First, determine the range of your data and divide it into equal-width bins. Then count how many data values fall into each bin. Finally, draw bars with heights equal to each bin's frequency, making sure the bars touch with no gaps between them.

Worked Examples

Example 1

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Test scores are grouped: 50–59 (4), 60–69 (8), 70–79 (12), 80–89 (6), 90–99 (2). Describe how to construct a histogram and identify the modal class.

Solution

  1. 1
    Step 1: The horizontal axis shows score intervals (no gaps between bars, unlike a bar graph). The vertical axis shows frequency.
  2. 2
    Step 2: Draw adjacent bars with heights 4, 8, 12, 6, 2 for each interval.
  3. 3
    Step 3: The modal class (tallest bar) is 70–79 with frequency 12.

Answer

Modal class is 70–79. Bars are adjacent with no gaps.
Histograms display the distribution of continuous or grouped numerical data. Unlike bar graphs, the bars touch because the intervals are continuous. The shape reveals the distribution.

Example 2

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A histogram of student heights shows bars: 140–149 cm (3), 150–159 cm (10), 160–169 cm (15), 170–179 cm (8), 180–189 cm (4). Describe the shape of the distribution.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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Explain two differences between a histogram and a bar graph.

Example 2

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A histogram shows frequencies 0–9 (2), 10–19 (5), 20–29 (9), 30–39 (7), 40–49 (1). How many observations are at least 20, and what is the modal class?
← Back to Histogram Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

bar graphstat range