Different data sets will have different means and standard deviations, so values from one set cannot always be compared directly with those from another. The z-score standardizes normally distributed data sets, allowing for a proper comparison and a consistent definition of percentiles across data sets. Z-scores can be found in a table, but using a TI-84 Plus calculator is easier and more accurate. There are two methods of finding the z-score of a data set: you can use the TI-84 Plus to find the mean and standard deviation and then use the z-score equation, or you can use the TI-84 Plus invNorm function with a percentile as the argument. The same process works with the TI-84 Plus Silver Edition calculator as well.

## Using the Z-Score Equation

1. Store your data set in the TI-84 Plus as a list by pressing STAT and then selecting 1:Edit from the menu. The screen will change to show the current lists and an entry line at the bottom of the screen. If less than three lists exist in the calculator memory, the screen will show empty columns.

2. Move the cursor to an empty list using the arrow keys if the list currently selected is not empty. Add each data point into the list by typing the value on the entry line and pressing ENTER.

3. Calculate the mean and standard deviation of the data set. Press STAT and then the right arrow key, which will bring up the menu for statistics calculations. Press 1 and then press ENTER to select 1-Var Stats. The screen will change to show the list name and the word CALCULATE.

4. Make sure the list name shown is the same list in which you entered your data. If it is not, use the arrow keys to move to the list name and type in the correct list. Leave FreqList blank.

5. Move the cursor to the word CALCULATE with the arrow keys and press ENTER. The screen will change again to show several statistics parameters, including the mean and standard deviation. Record these two parameters to use in the z-score equation.

6. Calculate the z-score by subtracting the mean from any data point in your list and then dividing that answer by the standard deviation.

## Using the invNorm Function

1. Press 2ND and then VARS to display the DISTR menu. Select 3 and press ENTER to bring up the invNorm wizard screen.

2. Enter the desired percentile as a decimal next to the word area. For example, to find the z-score associated with the 95th percentile, type 0.95. Use the arrow keys to select Paste and then press ENTER.

3. Press Enter again, and the TI-84 Plus will calculate the z-score associated with the chosen percentile.

References

Tips

- These instructions also work for the TI-84 Plus Silver Edition calculator.

About the Author

Joshua Bush has been writing from Charlottesville, Va., since 2006, specializing in science and culture. He has authored several articles in peer-reviewed science journals in the field of tissue engineering. Bush holds a Ph.D. in chemical engineering from Texas A&M University.