Final answer:
The number of classes in a frequency distribution for 53 observations can be estimated using Sturges' formula, suggesting around 6 classes. Practical considerations such as the range of data and class width are also important, with usually equal-width, continuous, non-overlapping intervals being the goal. Ultimately, it's about finding a balance between too few and too many classes.
Step-by-step explanation:
When organizing a set of data into a frequency distribution, one of the questions to consider is how many classes (or intervals) to use. A standard method to determine the number of classes is to use Sturges' formula, which is 1 + 3.322 log(N), where N is the number of observations in your data set. For 53 observations, this calculation would suggest around 6 classes, but this is just a rule of thumb.
However, in addition to mathematical rules, practical considerations should also be taken into account. Given that the range of the data is from 42 to 129, it is important to ensure that the class widths are manageable and that they cover the entire range. A possible approach is to divide the range by the number of classes to find the class width. In this situation, ensuring that each class has a sufficient number of data points without having too many classes to complicate the distribution is key.
It's also worth noting that each class interval should be continuous and non-overlapping, and it's common to aim for intervals that have an equal width. For example, if you chose to use 7 classes for the 53 data points with a range from 42 to 129, you would calculate the width of each class by subtracting the smallest value from the largest and then dividing by 7. As with all parts of statistical analysis, creating a histogram to visually inspect the distribution can help in deciding if the number of classes chosen was appropriate.