When drawing a histogram, which of the following statements is correct?

• A. The area of each bar is proportional to the $frequency$ of the corresponding class interval.
• B. The height of each bar always represents the $cumulative$ $frequency$.
• C. Bars in a histogram should be separated by gaps to distinguish different classes.
• D. The width of each bar must always be the same, regardless of class interval size.

Answer: (A)

Verified step by step guidance

1. Understand the purpose of a histogram: it is a graphical representation of the distribution of numerical data, where the data is divided into class intervals (bins).
2. Recall that in a histogram, the area of each bar represents the frequency of data points within that class interval. This means the height and width together determine the frequency representation.
3. Note that the height of each bar does not always represent cumulative frequency; instead, it typically represents frequency density (frequency divided by class width) when class widths vary.
4. Recognize that bars in a histogram should be adjacent without gaps because the data is continuous, and gaps would imply discontinuity between class intervals.
5. Understand that the width of each bar in a histogram can vary if class intervals are of different sizes, so the width is not always the same; the area (height × width) must be proportional to the frequency.