Which of the following best describes the purpose of a histogram?

• A. To summarize data using measures of central tendency only
• B. To show the relationship between two continuous variables
• C. To compare the means of two categorical variables
• D. To display the distribution of a quantitative variable by showing the frequency of data within specified intervals

Answer: (D)

Verified step by step guidance

1. Understand that a histogram is a graphical representation used in statistics to visualize the distribution of a quantitative (numerical) variable.
2. Recognize that a histogram groups data into intervals, called bins or classes, and displays the frequency (count) of data points that fall within each interval.
3. Note that histograms help identify patterns such as skewness, modality (number of peaks), and spread of the data, which are important aspects of the data's distribution.
4. Distinguish that histograms are not used to summarize data using only measures of central tendency (like mean or median), nor to show relationships between two variables, nor to compare means of categorical variables.
5. Conclude that the primary purpose of a histogram is to display the distribution of a quantitative variable by showing the frequency of data within specified intervals.