Final answer:
In a histogram, the area of each rectangle is indeed proportional to the frequency for a given class interval; it represents the number of data values within that interval. Histogram construction involves selecting suitable bin sizes and intervals thoughtfully to clearly represent the data distribution.
Step-by-step explanation:
It is correct to say that in a histogram, the area of each rectangle is proportional to the frequency of the corresponding class interval. This means that the area, which is the product of the class width (bin size) and the class frequency (height of the rectangle), represents the number of data values that fall within that interval. The histogram visually represents the distribution of the data, showing the shape, center, and spread of the data set. To ensure coherent interpretation, consistency in determining class intervals and their boundaries is crucial.
Some histograms count values that fall on the right boundary of an interval as part of that interval except for the last interval, or they may apply this rule universally across all intervals. The exact rules can vary, but the key idea is that each data value should be counted in exactly one interval.
When constructing a histogram, selecting the number of bins and the bin size is partially subjective, with clarity and ease of understanding being important factors to consider. Additionally, rounding or choosing an appropriate bin size can prevent data values from falling on interval boundaries, ensuring that each value is clearly categorised within a single interval.