I am hoping someone can explain this to me as I am so confused with determining the number of class intervals you should have in a frequency distribution. Our text indicates that the recommended number of class intervals be at least 10 but no more than 20, with 15 classes being the preferred average. It goes on to states that the number of recommended classes is only a rule of thumb and that the number must be based on the data and the interpretations that are to be drawn from these data.

I then encounter my first homework question:

What is the most appropriate number of class intervals for scores ranging from 21 to 85?

(A) 3 (B) 4 (C) 5 (D) 6

Since none of these numbers fell between the 10 to 20 that was recommended by the text, I was immediately lost. So I headed to the internet to find some help. after researching a bit, I located a reference which recommended a 2 to the K rule. If I calculated this correctly, I came up with k=6, therefore, I selected (D) 6. When I turned in my homework, this answer is incorrect, apparently the correct answer is (C) 5. When I asked my teacher to please explain how we determine the number of class intervals that should be appropriate, I was told that each employer will have their own preference and when I begin to work somewhere they will tell me what format I should use. That was my answer. When I pressed on as to how I was to determine the correct number of intervals for this class, I was told in not so many words that she gives the data to the students and no instruction as to how to manipulate it and we are to come up with how to do it. Meanwhile, I have an incorrect answer to the above question and I have no earthly idea how we were to come up with (5) as the correct answer.

Can anyone help to explain to me how the number of class intervals used in a frequency distribution should be determined? Is there another formula that would make the correct answer to this question 5? I am so lost on this and I am very concerned that this is important info that I need to understand and that this will continue to come up throughout the rest of the class, so I really want to grasp how to do this. What am I missing?

Thanks in advance for any help or guidance you can offer.