# Standard Deviation on a TI-89

#### Background:

As we will see in class, there are two standard deviations (sometimes called sample SD and population SD).  For now (until about chapter 26) we will be interested in population SD, which we will call simply "SD" for our class.

Problem:  While many calculators find both types of SD's, the TI-89 has only the sample SD built in (the SD we will use only rarely).  The TI-89 calls the sample SD "stdDev."

Solution:  With a one-line command we can (semi) permanently program the TI-89 to also compute population SD's (the SD's we will use often).  This is because (as we will see), the two standard deviations are related - so we can use the built-in sample SD to compute the SD we want.
To do the "programming," just type the following sequence of keystrokes.  For letters, use the [alpha] button first, and look for the purple letters above the keys.

define sd(x)=stddev(x)*((dim(x)-1)/dim(x))
We will see:
 as we start typing the formula as we finish typing the formula after we press [ENTER]

Be sure to get the parenthesis right and the spelling correct; the "space bar" is above the (-) key.

This will stay "programmed" unless you let the batteries go totally dead.  (If you need to replace the batteries, do it before they are completely dead, while the calculator is turned off, and the program should be retained.)

#### Using the newly programmed sd:

To find the SD of the list:  10,20,8,16,14,18,12
type:   sd({20,8,12,10,18,14,16})

We will see:
 ...before we press [ENTER] ...after we press [ENTER]

be sure to get the parentheses and braces as shown.  The braces are above the parentheses keys.

so the SD of this list is 4.

We DO NOT need to reenter the program to use it again, just type sd({20,8,12,10,18,14,16}) again (or change the list to whatever you want).

### Short summary:

To semi-permanently program the calculator to use "sd" for population SD, type the line:   define sd(x)=stddev(x)*((dim(x)-1)/dim(x))
To find the SD of the list 20,8,12,10,18,14,16 type:   sd({20,8,12,10,18,14,16})

### Test yourself:

Try to get the standard deviation of   37.75, 38, 37, 38.5, and 37.5. You should get a standard deviation of 0.5.

## Bonus Topics:

### Mean and Median, and other computations:

To find the mean, median, and some other useful items for a list of data, you should first store the data in a list
For example, to store the data   20,8,12,10,18,14,16  in a list named b, type:
{20,8,12,10,18,14,16}

We will see:

Then to find the mean and median, respectively, type
mean(b)
median(b)

We will see:

To see further calculations, type
onevar b     ...and press enter (no result shows yet)
then type
showstat
 ...before we press [ENTER] ...after we press [ENTER]

...We see a small window displaying the mean , along with the sample standard deviation Sx  (not the SD we're primarily interested in) along with quartiles and median further down. (the arrow keys will scroll the window)