## The SDThe SD measures the spread about the AVE. To compute the SD you need to:- Find the AVE for the list.
- Find the list of DEVIATIONS from the AVE.
- Find the RMS for the list of deviations.
## RMS = Root-Mean-Square- 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)
## SD = Typical-Deviation-from-AVE## EXAMPLEConsider 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> Last modified: Thu Jun 1 11:05:30 EDT 2000