How to Find aZ Score on TI 84: A Step-by-Step Guide

In statistics, the z-score is a measure that describes a value’s position relative to the mean of a group of values, measured in terms of standard deviations. It’s an essential concept used in many areas of statistics, especially in hypothesis testing and probability analysis.

If you’re working with a TI-84 calculator and need to calculate z-scores, this guide will walk you through everything you need to know. We’ll explain what z-scores are, how to calculate them manually, and more importantly, How to Find aZ Score on TI 84 calculator using its built-in statistical functions.

What is a Z-Score?

Before diving into the TI-84 calculator functions, it’s essential to understand the concept of a z-score.

A z-score tells you how many standard deviations a data point is from the mean. It’s calculated using the formula: z=(X−μ)σz = \frac{(X – \mu)}{\sigma}z=σ(X−μ)​

Where:

• XXX = raw score or individual data point
• μ\muμ = population mean
• σ\sigmaσ = population standard deviation

For sample data, you would replace μ\muμ and σ\sigmaσ with the sample mean xˉ\bar{x}xˉ and sample standard deviation sss.

Why Use a TI-84 for Z-Scores?

The TI-84 graphing calculator is widely used in high school and college statistics courses. It can:

• Perform z-score calculations
• Graph normal distributions
• Calculate probabilities and areas under the curve
• Reduce manual calculation errors

Using a calculator like the TI-84 saves time, especially when dealing with multiple values or needing to visualize the normal distribution.

How to Find a Z-Score on TI-84 (Step-by-Step)

Let’s explore two different approaches for finding a z-score using the TI-84:

Method 1: Manually Calculating Z-Score Using TI-84’s Math Functions

If you have the mean and standard deviation, and you’re given a raw score (X), you can enter the z-score formula directly.

Steps:

1. Turn on your TI-84.
2. Press the “CLEAR” button to start with a blank screen.
3. Use the formula: z=(X−μ)σz = \frac{(X – \mu)}{\sigma}z=σ(X−μ)​
4. For example, if the raw score is 85, the mean is 70, and the standard deviation is 10:
   • Type: CopyEdit(85 - 70) / 10
   • Press ENTER
   • The result will be: CopyEdit1.5
   This means the score is 1.5 standard deviations above the mean.

Method 2: Using “invNorm” to Find Z-Score from Probability

The TI-84 also has a built-in function called invNorm, which lets you find a z-score associated with a given left-tail probability (area to the left of the z-score under a normal distribution curve).

This is helpful when you are given a percentile or probability, and you want to find the corresponding z-score.

Steps:

1. Press the “2nd” button.
2. Press “VARS” to access the “DISTR” menu.
3. Scroll down and select invNorm(. This should appear as option 3.
4. You’ll see: scssCopyEditinvNorm(
5. Enter the probability (area to the left of the z-score).
   • For example, to find the z-score corresponding to the 90th percentile: scssCopyEditinvNorm(0.90)
6. Press ENTER.
   • The result will be: scssCopyEdit1.2816 (approximately)
   This means a value at the 90th percentile is about 1.28 standard deviations above the mean.

Optional Parameters:

If you’re working with a non-standard normal distribution (i.e., not mean = 0 and standard deviation = 1), you can enter:

scssCopyEditinvNorm(area, mean, standard deviation)

Example:

scssCopyEditinvNorm(0.90, 70, 10)

This gives the raw score (X) at the 90th percentile for a normal distribution with mean 70 and standard deviation 10.

When to Use Each Method

Scenario	Use This Method
You have a raw score and want the z-score	Manual calculation with formula
You have a percentile or probability	Use invNorm on TI-84
You need to visualize the distribution	Graphing normal curve on TI-84
You’re dealing with multiple values	Use lists and the 1-Var Stats function

Tips for Accuracy

• Always check whether your distribution is standard (mean = 0, SD = 1) or custom.
• Use parentheses correctly when entering formulas.
• Make sure your calculator is in the right mode (NORMAL, FLOAT, DEGREE).
• Round your z-scores appropriately based on your course or context.

Common Mistakes to Avoid

• Forgetting to subtract the mean when using the formula.
• Misplacing parentheses, which can change the entire calculation.
• Confusing left-tail with right-tail probabilities when using invNorm.
• Assuming all distributions are standard normal without adjusting mean and standard deviation.

FAQs: How to Find a Z-Score on TI-84

1. Can the TI-84 calculate multiple z-scores at once?

Not directly. The TI-84 does not have a bulk z-score function, but you can input multiple values in a list and then use the formula individually or create a program if allowed.

2. What is the difference between “invNorm” and “normalcdf”?

• invNorm: Gives you the z-score (or value) corresponding to a probability.
• normalcdf: Calculates the probability between two values or under a section of the normal curve.

Use invNorm to find a z-score from a percentile, and normalcdf to find the probability from z-scores.

3. Is the z-score the same for sample and population data?

The formula is the same, but you must be sure to use:

• σ\sigmaσ for population standard deviation
• sss for sample standard deviation

This matters most when calculating manually or using lists with sample data.

4. Can I use the TI-84 to graph z-score distributions?

Yes, you can graph normal distributions and shade areas using the normalpdf or normalcdf functions. This is particularly helpful for visual learners and for verifying your answers5. What’s the best way to practice z-scores with a TI-84?

Try:

• Solving textbook problems using the calculator
• Using online z-score calculators to compare answers
• Exploring datasets and using TI-84 lists to calculate sample means and standard deviations, then manually apply the z-score formula

Conclusion

Knowing How to Find aZ Score on TI 84 is a valuable skill for any student or professional working with data and statistics. Whether you’re manually calculating using the formula or using built-in functions like invNorm, the TI-84 offers fast, reliable, and accurate results.

Understanding when and how to use each method can help streamline your statistical work and reduce errors. By mastering this skill, you’ll be better equipped to interpret and analyze data — a key skill in many academic and career paths.