why is the range 31.57 - 34.03 is not a good choice for class boundaries?
31.57-34.03 has no frequency approximation for example 0-9
It would be better if the boundaries were whole numbers rather than hundredths (e.g., 32-34). your interval size = 2.46.
The range 31.57 - 34.03 might not be a good choice for class boundaries in statistical analysis because it does not satisfy the requirements for creating meaningful and balanced intervals. Class boundaries are determined by the data range, which is the difference between the maximum and minimum values in the data set.
When selecting class boundaries, it is important to consider a few factors such as the distribution of the data and the desired level of detail in the intervals. A good choice of class boundaries should provide a clear representation of the data and help in understanding its characteristics.
Here's a step-by-step explanation of how class boundaries are usually determined:
1. Find the range: Calculate the difference between the maximum and minimum values in your data set. In this case, the range is 34.03 - 31.57 = 2.46.
2. Decide on the number of classes: Determine the number of intervals, or classes, you want to divide your data into. This decision depends on the purpose of your analysis. A commonly used rule is to use the square root of the number of observations in your data set.
3. Calculate the class width: Divide the range by the number of classes to determine the class width. For example, if you decide to have 5 classes, the class width would be 2.46 / 5 = 0.492.
4. Determine the class boundaries: Starting from the minimum value, add the class width successively to determine the upper boundary of each class. For example, if the minimum value is 31.57 and the class width is 0.492, the class boundaries could be 31.57 - 31.57 + 0.492, 31.57 + 0.492 - 31.57 + 2 * 0.492, 31.57 + 2 * 0.492, and so on.
In the case of the range 31.57 - 34.03, if the class boundaries 31.57, 32.06, 32.55, and so on, do not provide a meaningful representation of the data or introduce unnecessary complexity, it might not be a good choice. It's important to consider the characteristics of your data and select class boundaries that effectively capture its distribution and patterns.