Which of the following best describes a key difference between a histogram and a bar graph?

• A. Both histograms and bar graphs require the data to be $\mathrm{continuous}$.
• B. A bar graph is used only for $\mathrm{numerical}$ data, while a histogram is used only for $\mathrm{categorical}$ data.
• C. A histogram always has $\mathrm{gaps}$ between the bars, while a bar graph never has $\mathrm{gaps}$.
• D. A histogram displays the $\mathrm{frequency}$ of data within $\mathrm{continuous}$ intervals, while a bar graph displays the $\mathrm{frequency}$ of data in $\mathrm{discrete}$ categories.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the purpose of a histogram. A histogram is used to display the frequency distribution of continuous numerical data, where data is grouped into intervals or bins.
2. Step 2: Understand the purpose of a bar graph. A bar graph is used to display frequencies or counts of discrete categories, which can be categorical or numerical but are distinct and separate groups.
3. Step 3: Recognize the visual difference. In a histogram, bars are adjacent with no gaps because the intervals represent continuous data ranges. In a bar graph, bars are separated by gaps to emphasize the distinct categories.
4. Step 4: Analyze the options given. The key difference is that histograms represent continuous data intervals, while bar graphs represent discrete categories, which aligns with the correct answer.
5. Step 5: Summarize the key distinction: A histogram shows frequency distribution over continuous intervals without gaps, whereas a bar graph shows frequency of distinct categories with gaps between bars.