# TI-83 Instructions

## Computing a Sample Variance and Standard Deviation

### Method 1 (Special keys)

- Press
`STAT`

.
- Select the
`CALC`

menu title.
- Select item #1,
`1-Var Stats`

.
- Press
`ENTER`

. The phrase `1-Var Stats`

appears in the display.
- Press
`2nd L`_{1}

.
- Press
`ENTER`

. A list of statistics appears.
The fourth one in the list, `Sx`

, is the sample standard deviation.
(Be careful not to use `σx`

. It represents the population standard deviation.)

### Method 2 (Alternative Formula)

- Enter the expression
`sum(L`_{1}^2) - sum(L_{1})^2

.
- Press
`÷`

(divide).
- Enter the sample size.
- Press
`ENTER`

.
- The display now shows the sum of the squared deviations, i.e.,
*SS*(*x*).
From here on, follow steps 11 - 17 under Method 3 below.

### Method 3 (Standard Formula)

- Compute the mean of
`L`_{1}

.
(See Computing a Mean.)
- Press
`L`_{1}

.
- Press
`-`

(minus).
- Enter the mean.
- Press
`ENTER`

. The display shows a list of deviations.
- Press
`STO`

.
- Press
`2nd L`_{2}

.
- Press
`ENTER`

. The deviations are now stored in list `L`_{2}

.
- Enter the expression
`sum(L`_{2}^2)

.
- Press
`ENTER`

. The display now shows the sum of the squared deviations,
i.e., *SS*(*x*).
- Press
`÷`

(divide).
- Enter one less than the sample size, i.e.,
*n*` - 1`

.
- Press
`ENTER`

. This gives the variance.
- Press the square root key. The square root symbol appears.
- Press
`2nd ANS`

. The expression `Ans`

appears after the square root.
This refers to the result of the previous calculation, which in this case is the variance.
- Press
`)`

.
- Press
`ENTER`

. The display now shows the standard deviation.