Histogram Math Example 1

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Example 1

easy
The following data represent exam scores: {52,64,68,71,75,75,78,82,85,88,90,93}\{52, 64, 68, 71, 75, 75, 78, 82, 85, 88, 90, 93\}. Group them into intervals [50,70),[70,80),[80,90),[90,100][50,70), [70,80), [80,90), [90,100] and describe how to construct a histogram.

Solution

  1. 1
    Count values in each interval: [50,70)[50,70): 52, 64, 68 → 3 values; [70,80)[70,80): 71, 75, 75, 78 → 4 values; [80,90)[80,90): 82, 85, 88 → 3 values; [90,100][90,100]: 90, 93 → 2 values
  2. 2
    Draw horizontal axis with interval boundaries (50, 70, 80, 90, 100) and vertical axis for frequency
  3. 3
    Draw touching bars (no gaps) with heights 3, 4, 3, 2 for each interval respectively
  4. 4
    Label axes: 'Score' on x-axis, 'Frequency' on y-axis

Answer

Histogram with bars of height 3, 4, 3, 2 over intervals [50,70),[70,80),[80,90),[90,100][50,70),[70,80),[80,90),[90,100].
Histograms display the distribution of quantitative data. Unlike bar charts, bars touch to show continuous data. The height represents frequency (or relative frequency). The shape reveals skewness, modes, and spread.

About Histogram

A histogram is a bar chart of a frequency distribution where bars represent count or density of data within consecutive equal-width intervals (bins).

Learn more about Histogram →

More Histogram Examples

Example 2 medium

A histogram of household incomes is skewed right. Describe what this means and explain why the mean

Example 3 easy

A histogram has bars at intervals [formula] with frequencies 5, 12, 8, 3. What is the total number o

Example 4 hard

Two histograms of test scores have the same mean (75) but different shapes: one is symmetric and bel

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Related Concepts

Normal Distribution