# TI-82: Statistics using Lists

All of the following examples assume the data values are in List 1. All of the functions used here are under the LISTS menu.

## Measures of Central Tendency

### Mean

`   SUM L1 / DIM L1`

or, even easier

`   MEAN( L1 )`

### Median

`   MEDIAN( L1 )`

### Midrange

`   ( MAX( L1 ) + MIN( L1 ) ) / 2`

## Measures of Variation

### Range

`   MAX( L1 ) - MIN( L1 )`

### Sample Variance

`   ( SUM L1^2 - ( SUM L1 )^2 / DIM L1 ) / ( DIM L1 - 1 )`

### Population Variance

`   ( SUM L1^2 - ( SUM L1 )^2 / DIM L1 ) / DIM L1`

### Standard Deviation

To find either standard deviation, first find the corresponding variance, and take the square root of the answer. To take the square root, press: 2nd x2 and 2nd (-).

Alternatively, start the equation for the variance off with a square root and an extra left parenthesis ")". End the expression with an extra right parenthesis ")".

## Measures of Position

### Standard Scores

Once you have the mean and standard deviation computed, you can compute standard scores. The following assumes that you have saved the mean into M and the standard deviation into S.

`   ( L1 - M ) / S`

### Sorting the Data

Most measures of position require the data to be ranked in order from smallest to highest.

Note that sorting will rearrange the data. If you need to keep a copy of the data in its original order, then you need to make a backup copy first.

`   L1 STORE L2`

To accomplish the ranking of data, sort the list: You may sort more than one list at a time by separating them with commas.

`   SORTA( L1 )`

### Percentiles, Deciles, Quartiles

To find the kth percentile, follow the following steps:

1. Divide k by 100 and multiply by the sample size.
2. If this number is an integer, add 0.5 and take the mean of the numbers in those two positions.
3. If this number is not an integer, round up and take the number in this position

#### Example 1:

Find the 40th percentile with a sample size of 19.

`   0.40 * 19`

The answer is 7.6. This is not an integer, so round up to 8. Find the number in the eighth position.

`   L1(8)`

#### Example 2:

Find the 40th percentile with a sample size of 20.

`   0.40 * 20`

The answer is 8. This is an integer, so add 0.5 to make it 8.5. Find the mean of the numbers in the 8th and 9th positions.

`   ( L1(8) + L1(9) ) / 2`

#### Deciles

Deciles divide the data set into ten parts. So, instead of dividing by 100, as you do for percentiles, divide by 10. The rules about rounding up or adding 0.5 are the same.

#### Quartiles

Quartiles divide the data set into four parts. So, instead of dividing by 100, as you do for percentiles, divide by 4. The rules about rounding up or adding 0.5 are the same.

### Box and Whiskers Plot

You can obtain the minimum, 1st quartile, median, 3rd quartile, and maximum values from the box and whiskers plot. The procedure for finding the box and whiskers plot on the TI-82 was explained before.

There is no way to easily obtain the hinges using the TI-82 except to sort the data and then manually compute the values.

### Interquartile Range (IQR)

Once the values of the quartiles are determined, you can easily compute the Interquartile Range by taking the difference between the third and first quartiles.

## Other ways to find the information

The above explanation tells how to find the values using the lists on the calculator. There is also a statistics mode which will find many of the statistics for you.