A z-score is a measure of how many standard deviations a given value is away from the mean of a distribution. It is calculated as:
z = x−μ/σ
where x is the individual value, μ is the population mean, and σ is the population standard deviation.
Finding z-scores on a ti-84 calculator is easy and can be done in two ways: using a formula or using a list of data values. In this article, we will explain both methods with examples.
Using a formula
If you have a single value and you know the mean and standard deviation of the distribution, you can use a formula to find the z-score. For example, suppose a distribution is normally distributed with a mean of 12 and a standard deviation of 1.4 and we wish to calculate the z-score of an individual value x = 14.
To find the z-score using a formula, follow these steps:
- Press the
ONbutton to turn on the calculator. - Press the
MODEbutton and make sure thatNORMALis selected for the display mode. - Press the
2NDbutton and then press the0button to access the catalog of functions. - Scroll down until you see the
Z-Testfunction and pressENTERto select it. - Press the
2NDbutton and then press theVARSbutton to access the distribution menu. - Scroll down until you see the
normalcdf(function and pressENTERto select it. - Enter the value of x, the mean, and the standard deviation separated by commas. For our example, we would enter
14,12,1.4. - Press the
)button to close the parentheses and pressENTERto calculate the z-score.
The calculator will display the z-score as 1.428571429. This means that the value 14 lies 1.4286 standard deviations above the mean.
Using a list of data values
If you have a list of data values and you want to find the z-score for every value in the list, you can use the following steps:
- Press the
ONbutton to turn on the calculator. - Press the
STATbutton and then press theEDITbutton to access the data editor. - Enter the data values in column L1. For example, suppose we have the following data values: 3, 4, 7, 10, 11, 13, 15, 16, 18, 20.
- Press the
STATbutton and then scroll over to theCALCmenu. - Highlight the
1-Var Statsoption and pressENTERto select it. - For
List, make sure L1 is chosen since this is the column we entered our data in. LeaveFreqListblank. - Highlight
Calculateand pressENTERto find the summary statistics of the data values. - The calculator will display the mean and the standard deviation of the data values as
x = 10.7andsx = 5.558038. We will use these values to calculate the z-scores. - Press the
STATbutton and then press theEDITbutton to go back to the data editor. - Highlight L2 and type in the formula
(L1-10.7) / 5.558038and then pressENTER. The z-score of every individual value will automatically appear in column L2.
The calculator will display the z-scores as follows:
| x | z |
|---|---|
| 3 | -1.388 |
| 4 | -1.208 |
| 7 | -0.667 |
| 10 | -0.126 |
| 11 | 0.054 |
| 13 | 0.414 |
| 15 | 0.774 |
| 16 | 0.954 |
| 18 | 1.314 |
| 20 | 1.674 |
This means that, for example, the value 3 is 1.388 standard deviations below the mean, and the value 20 is 1.674 standard deviations above the mean.
Summary
In this article, we learned how to find z-scores on a ti-84 calculator using two methods: using a formula and using a list of data values. Z-scores are useful for comparing values from different distributions or for finding the probability of a value under a normal curve. We hope this article was helpful and informative. For more information on z-scores and other statistical concepts, you can check out this website.