Which of the following statements about histograms is true?

• A. In a histogram, the height of each bar represents the $\mathrm{mean}$ of the data in that bin.
• B. Histograms can be used to display the frequencies of categorical variables.
• C. Histograms are used to display the distribution of a quantitative variable by grouping data into bins.
• D. The bars in a histogram are always separated by gaps to indicate distinct categories.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand what a histogram represents. A histogram is a graphical representation used to display the distribution of a quantitative (numerical) variable by grouping data into intervals called bins.
2. Step 2: Recognize that in a histogram, the height of each bar corresponds to the frequency (count) or relative frequency of data points within that bin, not the mean of the data in that bin.
3. Step 3: Note that histograms are not suitable for categorical variables because categories are distinct and non-numeric; instead, bar charts are used for categorical data, where bars are separated by gaps.
4. Step 4: Remember that in histograms, bars are adjacent (no gaps) because the bins represent continuous intervals of data, emphasizing the continuous nature of the variable.
5. Step 5: Conclude that the true statement is: 'Histograms are used to display the distribution of a quantitative variable by grouping data into bins.'