The SD explained

The SD

The SD measures the spread about the AVE. To compute the SD you need to:

The RMS of a list of numbers measures the typical size of an entry in the list disregarding signs. To compute the RMS just read it backwards... i.e.

take the Square of the entries in the list. (this amplifies the values but kills the negative signs)
take the Mean of the squares. (this gives a middle square value)
take the squareRoot. (this undoes the amplification of the first step)

Hence,

Consider the following list

> L := -1,3,6,9,13;

                             L := -1, 3, 6, 9, 13

Let's follow each of the three steps (given above) to compute the SD.

> AVE := (-1 + 3 + 6 + 9 + 13)/5;

                                  AVE := 6

The list of DEVIATIONS from the AVE is obtained by substracting the AVE from each entry of the original list,

> Dev := -1-AVE, 3-AVE, 6-AVE, 9-AVE, 13-AVE;

                            Dev := -7, -3, 0, 3, 7

Now the SD will be RMS of the list above. To compute the RMS we take the Squareroot-of-the-Mean-of-the-Squares...

> RMS := sqrt(((-1-AVE)^2+(3-AVE)^2+(6-AVE)^2+(9-AVE)^2+(13-AVE)^2)/5.);

                              RMS := 4.816637832

And this RMS is the value of the SD.

Last modified: Thu Jun 1 11:05:30 EDT 2000