# The SD

The SD measures the spread about the AVE. To compute the SD you need to:
1. Find the AVE for the list.
2. Find the list of DEVIATIONS from the AVE.
3. Find the RMS for the list of deviations.

## RMS = Root-Mean-Square

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,

# EXAMPLE

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.

## SD = 4.8

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>