Final answer:
The acceptable formats for setting up class boundaries for a frequency distribution are equal width intervals, equal frequency intervals, and arbitrary intervals. Using no intervals is not an option for histograms, and values on the boundaries are typically included in the interval to the left.
Step-by-step explanation:
The acceptable formats for setting up class boundaries for a frequency distribution include equal width intervals, equal frequency intervals, and arbitrary intervals. Each format has its own application depending on the nature of the data and the purpose of the analysis. The use of intervals, however, is necessary for creating histograms – no interval approach is generally not an option when dealing with frequency distributions. When constructing histograms, it's also essential to be consistent in counting the data values that fall on boundaries, typically including them in the left interval but not if they fall on the right boundary, except for the first interval where both may be included.
As noted in various references, there is more than one correct way to set up a histogram, and different researchers may present the same data in different formats. Regardless of the interval type chosen, the goal is always to represent the data in a meaningful and understandable way that aids in the analysis.