When constructing a frequency distribution, do I find the class limit which will

Question

When constructing a frequency distribution, do I find the class limit which will tell me how many sections my frequency distribution will have?

Also when I find the class width, do I use it to set the range of the frequency distribution?

for example:
22.4, 25, 12.7, 33, 15, 37, 30, 26, 14, 13

5 classes are to be formed. find the lower class limit for the first class and a class width.

class width : (37-12.7)/5 = 4.86

lower limit: 5 or is it 12( this is because there are supposed to be 5 classes right or is it because I round the width? Or is it the lowest possible number in the list which should be 12? )

So from here I create my frequency distribution like this:
(this is where I use the class width to get the range in between the numbers?)
(12 - 16.87 or 16.99) = 4
(17- 21.87 or 21.99) = 0
(22-26.87 or 26.99) = 3
(27-31.87 or 31.99) = 1
(32-36.87 or 36.99) = 1

At this point 37 is left out. what do I do then?

Explanation / Answer

We do not fix lower and upper limits according to given numbers. Just keep in mind that these limits should be near to the smallest and largest numbers of the given data respectively.

Here if we take lower limit =12

class width = 6

Upper limit = 12+6*5=12+30=42

In this way our frequency distribution will become

Class intervals                Frequency

12-17                                4

18-23                                1

24-29                                 2

30-35                               2

36-41                                 1

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