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

• A. A histogram uses bars of varying widths, while a bar graph always uses bars of equal width.
• B. A histogram displays the frequency of data within continuous intervals, while a bar graph displays the frequency of data in discrete categories.
• C. A histogram always has gaps between the bars, while a bar graph does not.
• D. A histogram is used only for categorical data, while a bar graph is used only for numerical data.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the purpose of a histogram. A histogram is used to display the frequency distribution of numerical data that is continuous, 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 categorical (discrete) data, where each bar represents a distinct category.
3. Step 3: Note the visual differences. In a histogram, bars are adjacent with no gaps because the intervals are continuous, while in a bar graph, bars are separated by gaps to emphasize distinct categories.
4. Step 4: Recognize that the width of bars in a histogram corresponds to the class intervals and is usually consistent, but the key is that the data is continuous; in bar graphs, bars represent categories and are always of equal width.
5. Step 5: Summarize the main difference: A histogram displays frequencies of continuous data grouped into intervals (with bars touching), whereas a bar graph displays frequencies of discrete categories (with gaps between bars).