[College Statistics: Frequency Distribution] Determining the cases for a frequency distribution

[bbl]

The problem is, "A set of data consists of 64 observations. How many classes would you recommend for the frequency distribution?"

I know that I can use the 2 to the k rule for this. There are 64 observations since 2^6 = 64 and 2^7 = 128, is it correct for me to recommend using 7 cases since the 2 to the k rule states that 2^k is greater than the number of observations, where k is the smallest integer.

Any help is appreciated. Thank you!

 

[Dr.Peterson]

The problem is, "A set of data consists of 64 observations. How many classes would you recommend for the frequency distribution?"

I know that I can use the 2 to the k rule for this. There are 64 observations since 2^6 = 64 and 2^7 = 128, is it correct for me to recommend using 7 cases since the 2 to the k rule states that 2^k is greater than the number of observations, where k is the smallest integer.

Any help is appreciated. Thank you!

This is a subjective question; no one answer is necessarily right. It appears you have been given some rules of thumb, but they are not universal.

Please show the "rules" you have been taught, so we can see what the authors consider important. Your answer has to satisfy your teacher, not us! In particular, I can see some reason for the rule you cite, but I don't see why it would not use "greater than or equal", that is, [imath]2^k\ge n[/imath]. In fact, when I search for "2^k rule" most sources I see have it in that form, for example here.

Searching further, out of curiosity, I find that this rule is equivalent to something called Sturges' Rule, which is explained and sort of debunked here: The problem with Sturges’ rule for constructing histograms

I'd never heard of either until now.

 

[bbl]

This is a subjective question; no one answer is necessarily right. It appears you have been given some rules of thumb, but they are not universal.

Please show the "rules" you have been taught, so we can see what the authors consider important. Your answer has to satisfy your teacher, not us! In particular, I can see some reason for the rule you cite, but I don't see why it would not use "greater than or equal", that is, [imath]2^k\ge n[/imath]. In fact, when I search for "2^k rule" most sources I see have it in that form, for example here.

Searching further, out of curiosity, I find that this rule is equivalent to something called Sturges' Rule, which is explained and sort of debunked here: The problem with Sturges’ rule for constructing histograms

I'd never heard of either until now.

Thank you so much for the reply! Here is what we were taught:

 

[Dr.Peterson]

Thank you so much for the reply! Here is what we were taught: View attachment 29618

Taking what they say literally, what you did is correct by their rule, though being on the edge, you would still be justified in going either way. In any case, it is presented only as "one way", and a choice. (I suspect that not all teachers would recognize this, however.)

The rule I found elsewhere could be expressed as "the smallest integer k so that 2^k is at least equal to the number of observations", and 6 would be an acceptable answer (though, again, you would be justified in adding 1).

Oddly enough, by the version of Sturges' rule I found, the answer would be [imath]k = 1 + log_2 n = 1 + log_2 64 = 7[/imath]. That rule doesn't say how to round the result, but rounding isn't needed here.

 

[bbl]

I see! My teacher's rule is a bit odd, I agree, since I mostly come across ones with "greater than or equal" but thank you for your additional insight!