Histogram Statistics Example 2

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Example 2

medium
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.

Solution

  1. 1
    Step 1: Frequencies increase from left: 3, 10, 15, then decrease: 8, 4.
  2. 2
    Step 2: The peak is at 160–169 cm, with the data tapering on both sides.
  3. 3
    Step 3: This is approximately a bell-shaped (symmetric) distribution, slightly skewed right since the right tail (8, 4) drops off slightly faster.

Answer

Approximately symmetric (bell-shaped), centred around 160–169 cm.
The shape of a histogram tells us about the distribution: symmetric, left-skewed, or right-skewed. This helps us decide which summary statistics (mean vs median) are most appropriate.

About Histogram

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.

Learn more about Histogram →

More Histogram Examples

Example 1 medium

Test scores are grouped: 50–59 (4), 60–69 (8), 70–79 (12), 80–89 (6), 90–99 (2). Describe how to con

Example 3 medium

Explain two differences between a histogram and a bar graph.

Example 4 medium

A histogram shows frequencies 0–9 (2), 10–19 (5), 20–29 (9), 30–39 (7), 40–49 (1). How many observat

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