I believe they want you to create categories of 4 integers each and then group the data into those categories.
since your minimum number is 64 and your maximum number is 87, i created categories of 4 numbers each as follows:
category min max number
1 64 67 3
2 68 71 4
3 72 75 7
4 76 79 7
5 80 83 2
6 84 87 5
class width i believe is just another name for category.
each category has a width of 4 integers.
the midpoint of each category would generally be the number assigned to that category.
if so, midpoints for each category would be defined as shown below:
category min max frequency midpoint
1 64 67 3 65.5
2 68 71 4 69.5
3 72 75 7 73.5
4 76 79 7 77.5
5 80 83 2 81.5
6 84 87 5 85.5
the differences between data that is grouped and data that is not grouped are:
data that is grouped has less volume.
data that is not grouped is more accurate.
as an example:
the average of the data that is not grouped is the sum of the data divided by the number of elements in the data.
those numbers are:
total 2119
count 28
average 75.67857143
the average of the data that is grouped is the sum of the midpoint of each category multiplied by the number of items in that category and then divided by the total number of elements.
those numbers are:
total 2122
count 28
average 75.78571429
to undersytand what's different, we'll take one of the categories and show you the detailed calculation for the data that is grouped and the same data that is not grouped.
we'll take the category of 1.
that is the number that are between 64 and 67 inclusive.
there are 3 numbers that comprise that category.
those numbers are:
64
67
67
the average of these 3 numbers, by themselves is 64 + 67 + 67 = 198/3 = 66
the average of this group, taken by itself, would be:
65.5 * 3 / 3 = 65.5
here's a reference you might find useful:
http://www.mathsisfun.com/data/frequency-distribution-grouped.html
