Given a frequency histogram showing the number of students who scored within each $10$-point interval on a test, which of the following statements is correct about the distribution of scores?

• A. The height of each bar represents the number of students in that score interval.
• B. The histogram can be used to determine the exact score of each student.
• C. The area of each bar represents the cumulative frequency up to that interval.
• D. The width of each bar represents the mean score of the interval.

Answer: (A)

Verified step by step guidance

1. Understand what a frequency histogram represents: it displays the distribution of data by grouping scores into intervals (bins) and showing how many data points fall into each interval.
2. Recall that in a frequency histogram, the height of each bar corresponds to the frequency (number of observations) within that interval, while the width of each bar represents the class interval size (e.g., 10 points).
3. Recognize that the area of each bar in a frequency histogram is proportional to the frequency because area = height × width, but the area does not represent cumulative frequency; cumulative frequency is the total number of observations up to a certain interval and is typically shown in a cumulative frequency graph, not a histogram.
4. Note that a histogram does not provide exact individual scores; it only shows how many scores fall within each interval, so you cannot determine the exact score of each student from the histogram alone.
5. Understand that the width of each bar is fixed by the interval size and does not represent the mean score of the interval; the mean score would be a single value calculated separately from the data.