How to Find the Z Score on a TI 84

The Z score is a key concept in statistics that shows how far a value is from the mean in terms of standard deviations. If you’re using a TI 84 calculator, it’s easy to calculate Z scores either manually or using built-in functions.

In this guide, you’ll learn how to find the Z score on a TI 84, with step-by-step instructions and examples that are perfect for students and teachers alike.

What Is a Z Score?

A Z score tells you how many standard deviations a data point is from the mean. The formula is:

Z = (X - μ) / σ

Where:

• X = individual data point
• μ = mean of the dataset
• σ = standard deviation of the dataset

When Do You Use Z Scores?

Z scores are commonly used in:

• Normal distribution problems
• Standardizing test scores
• Comparing scores from different distributions
• Probability calculations

Method 1: Manually Calculate the Z Score on a TI 84

Step 1: Input the Data

Use this example:

• X = 80
• Mean (μ) = 70
• Standard deviation (σ) = 5

Step 2: Use the Z Score Formula

Press ( then type:

(80 - 70) ÷ 5

So on your calculator:

(80 - 70) ÷ 5 → ENTER

Result:

Z = 2

This means the value is 2 standard deviations above the mean.

Method 2: Calculate Mean and Standard Deviation Automatically

If you have a list of numbers and want to find the Z score of one data point:

Step 1: Enter Data into Lists

1. Press STAT → 1:Edit
2. Enter your data in L1

Example:

65, 70, 75, 80, 85

Step 2: Find Mean and Standard Deviation

1. Press STAT → Arrow right to CALC
2. Select 1:1-Var Stats → Press ENTER
3. Type L1 by pressing 2nd then 1
4. Press ENTER

You’ll get values like:

• x̄ = 75 (mean)
• σx = 7.07 (standard deviation)

Step 3: Plug into Z Score Formula

If you want to find the Z score of 80, use:

Z = (80 - 75) ÷ 7.07

So on the calculator:

(80 - 75) ÷ 7.07 → ENTER

Result: Z ≈ 0.71

Method 3: Using Normalcdf and invNorm (Advanced)

While these don’t directly give a Z score from raw data, they’re helpful for probability and percentile problems.

To find the Z score for a given percentile:

1. Press 2nd → VARS (DISTR)
2. Choose 3:invNorm(
3. Type the percentile (as a decimal), for example:

InvNorm(0.90)

4. Press ENTER

This gives you the Z score for the 90th percentile:

Z ≈ 1.28

Real-Life Example

Problem:
A test has a mean of 100 and standard deviation of 15. What is the Z score of a student who scored 130?

Solution:

Z = (130 - 100) ÷ 15 = 2

Interpretation:
The student scored 2 standard deviations above the average.

Common Mistakes to Avoid

• Don’t confuse population (σ) and sample (Sx) standard deviations
• Make sure to use parentheses in calculations
• Always check if your calculator is in normal mode, not scientific

Conclusion

Finding the Z score on a TI 84 calculator is straightforward whether you’re using raw data or summary stats. You can either calculate it manually using the formula or rely on built-in features like 1-Var Stats for speed.

Z scores are essential for understanding how individual values relate to the rest of the data, especially in standardized testing and probability questions.