For performing statistical analysis and graphing a series of data points, it is best if you present the data in an orderly fashion. The way to do this is to make a histogram, which is basically presenting the myriad data points you may have as a series of easy to handle categories.

Within those categories fall all your data points. So if you were building a scientific study to measure kids heights as they grow up, you would end up with hundreds of data points of ages and heights for every kid you measure. To make a histogram is to categorize for example Heights from 0 to 1 foot, "Heights from 1 foot to 2 feet", "Heights from 2 feet to 3 feet" and so on. You would probably only reach to about "Heights from 6 feet to 7 feet" because that's where the majority of the human race falls, right? So you categorized hundreds of data points into 6 or 7 categories, and all you have to do is add the data points that fall into each category and then graph the categories against the sum of the data points in them: what is called a Histogram.

Now, this method you present is a sub that takes as an input the variable M and the array arr(). As variable M, you need to pass the number categories that you want to have. This number is not by magic, there are a few methods to obtain the optimum number of categories for a given data set.

As variable arr() you pass the values of the ordered data points. It is important that they have to be in order, from lower number to higher number (that you achieve with a basic sort on the spreadsheet). If your ordered data points are (1, 1.2, 1.3, 1.4, 1.6, 2.1, etc) you pass that to the method as an array.

Now, the method does the following with those numbers:

Dim i As Long, j As Long

Dim Length As Single

ReDim breaks(M) As Single

ReDim freq(M) As Single

1) It initializes variables that will be used

For i = 1 To M

freq(i) = 0

Next i

2) It sets the array freq to zeroes (this is unnecesary as it already is initialized to zero when you Dim it)

Length = (arr(UBound(arr)) - arr(1)) / M

3) It takes the highest data point, substracts the lowest data point from it, and divides the result by the number of categories you want to have. So if your tallest kid is 5.4 and your lowest 1.4, and you want 4 categories, the result would be (5.4-1.4)/4 which is 1. That is the length of the 4 categories (from 1 to 2, from 2 to 3, from 3 to 4 and from 4 to 5, for example)

For i = 1 To M

breaks(i) = arr(1) + Length * i

Next i

4) It calculates the categories for your data points based on the previous result. It sets M number of categories (remember M was passed to the method). It begins with the lowest value (say 1.4 in our example) and it adds the length, so it ends up with 4 categories: 1.4 to 2.4, 2.4 to 3.4, 3.4 to 4.4 and 4.4 to 5.4). Notice that it ends, not by miracle, on 5.4 which is the tallest kid's measure. It stores all this in the breaks() array

For i = 1 To UBound(arr)

If (arr(i) <= breaks(1)) Then freq(1) = freq(1) + 1

If (arr(i) >= breaks(M - 1)) Then freq(M) = freq(M) + 1

For j = 2 To M - 1

If (arr(i) > breaks(j - 1) And arr(i) <= breaks(j)) Then freq(j) = freq(j) + 1

Next j

Next i

5) This is the frequency counter. Basically it begins to count, of all your data points, how many fall into the first category, how many to the second, and so on. It loops from 1 to ubound(arr), which in our case is 4, once per category. If the data point is below the category, it adds 1 to the freq() array, if it is above the last category it adds one to the final category. For everything in between the first and last, it loops from the second to the final minus one category and performs the counts.

For i = 1 To M

Sheet3.Cells(i + 9, 10) = breaks(i)

Sheet3.Cells(i + 9, 11) = freq(i)

Next i

6) it copies the result to sheet3

Hope this was of some help, let me know if you need more detail...

NY