first of all - im from germany, sry if my english is not perfect

ive got a problem with the class intervals...

a little example:

A set of data consists of 230 observations between $235 and $567. What class interval

would you recommend?

So i would refer to the “2 to the k rule", that means if i take the number 8, i would have a result of 2^8 = 256 which is bigger than my number of observations...

now i would compute the range (567-235)=332 and divide this number by 8 (as i have chosen this number as my class size) which is 41.5, rounded up is it 42...

i cannot see my mistake, but in my master-solutions i have the number 30 as a class size, so i have class intervals of 235-265 and so on...

so what am i doing wrong??

another example is this task:

A set of data contains 53 observations. The lowest value is 42 and the largest is 129.

The data are to be organized into a frequency distribution.

I have 6 as a number of classes, and so i would calculate (129-42)/6 ) = 14.5, rounded up it is 15, but my teacher has 9 classes as a solution

what is wrong, or what can i change??

LG (dont know how to greet in english haha)