How to Find Z-Score on TI-84?

The TI-84 calculator simplifies z-score calculations, which measure how many standard deviations a data point is from the mean. Whether you have a physical calculator or prefer using an online TI-84 calculator, the following methods will help you compute z-scores efficiently.

Quick Tip: Don't have a physical TI-84? Try the free online TI-84 calculator to follow along with these instructions. It works exactly like a physical calculator and is accessible from any device!

Below are two primary methods to compute z-scores, applicable to both individual values and entire datasets.

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Method 1: Using the Z-Score Formula

Formula:
$z = \frac{x - \mu}{\sigma}$
where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Steps for a Single Value:

1. Calculate Mean and Standard Deviation:

   • Press STAT > 1:Edit to enter your dataset into a list (e.g., L1).

   • Press STAT > CALC > 1-Var Stats, select your list (e.g., L1), and press ENTER.

   • Record the mean ($\mu$) and standard deviation ($\sigma$) from the results.

   Note: If you're using the online TI-84 calculator, the interface and buttons work identically to the physical calculator, making it easy to follow these steps.

2. Compute the Z-Score:

   • Use the formula $z = \frac{x - \mu}{\sigma}$. For example, if $\mu = 12$, $\sigma = 1.4$, and $x = 14$, the z-score is:
     $z = \frac{14 - 12}{1.4} \approx 1.4286$
     This means 14 is 1.4286 standard deviations above the mean.

Steps for Multiple Values:

1. Enter Data:

   • Input all data points into a list (e.g., L1).

2. Calculate Mean and Standard Deviation:

   • Follow the same 1-Var Stats process as above.

3. Automate Z-Scores for a List:

   • Highlight L2 and enter the formula: (L1 - [mean]) / [standard deviation].
     • Example: If (\mu = 10) and (\sigma = 5.558), type (L1 - 10) / 5.558.
   • Press ENTER to display z-scores for all values in L2.

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Method 2: Using the invNorm Function

This method calculates the z-score for a given percentile (area under the normal curve).

Steps:

1. Access invNorm:

   • Press 2ND > VARS > 3:invNorm.

2. Input Percentile:

   • Enter the desired percentile as a decimal (e.g., 0.95 for the 95th percentile).
   • Select Paste and press ENTER twice.

3. Result:

   • The calculator returns the z-score. For example, invNorm(0.95) ≈ 1.645, indicating the 95th percentile corresponds to 1.645 standard deviations above the mean.

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Interpreting Z-Scores

• Positive z-score: Value is above the mean.
• Negative z-score: Value is below the mean.
• Zero z-score: Value equals the mean.

For example, a z-score of -1.259 means the data point is 1.259 standard deviations below the mean.

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Common Mistakes to Avoid

• Formula Errors: Ensure correct order: $z = \frac{x - \mu}{\sigma}$, not $\frac{\mu - x}{\sigma}$.
• List Entry: Use 2ND > 1 to input "L1" in formulas.
• Percentile Input: Always use decimals (e.g., 0.75 instead of 75).
• Calculator Access: If you don't have immediate access to a physical TI-84, remember you can use the online TI-84 calculator to practice these calculations anytime, anywhere.

By mastering these methods, you can efficiently analyze datasets, compare values across distributions, and interpret statistical results using either a physical TI-84 or the convenient online version.