Final answer:
Class width in a frequency distribution is the range of data values within each class or bin, vital for constructing histograms. It can be calculated by dividing the total range by the number of desired intervals, and it's important to ensure values don't fall on class boundaries for clarity.
Step-by-step explanation:
The class width in a frequency distribution is defined by the range of values contained within each class or bin and is a critical aspect of creating histograms. When setting up a histogram, consistency is important in how the boundaries of these classes are treated. Some histograms count values that fall on the right boundary within the class interval while excluding those on the left, with the exception of the first interval, where both boundaries might include values. Although it is common to round the class width to prevent data points from falling on the boundaries, there are also methods such as using the square root of the number of data points to estimate the number of class intervals which can then determine the class width.
In the case of constructing a histogram for a data set with a range of 68 values (from 32.5 to 100.5), and a desired number of 5 intervals, the class width would be calculated as (100.5 - 32.5) / 5, which equals 13.6. Therefore, each interval would span 13.6 units along the axis of the histogram, ensuring that none of the data values fall on an interval boundary, thereby providing clarity within the visual representation.