Calculate Z Score Ti 84 Negative Z Score

What is a Z-Score?

A z-score (also called a standard score) measures how many standard deviations an element is from the mean. Z-scores transform data into a standard normal distribution with a mean of 0 and standard deviation of 1, making it easier to compare different datasets.

The formula for calculating a z-score is:

When the z-score is negative, it indicates that the data point is below the mean of the distribution.

Understanding Negative Z-Scores

A negative z-score means the data point is below the mean. For example, if you have a test score that's 1 standard deviation below the average, your z-score would be -1.0.

Negative z-scores are common in:

• Test scores below average
• Height measurements below average
• Income levels below the mean
• Any measurement that's below the norm

How to Calculate on TI-84

Calculating a z-score on your TI-84 is straightforward. Here's a step-by-step guide:

1. Enter your data into the TI-84's list editor (STAT → Edit)
2. Calculate the mean (μ) using STAT → Calc → 1-Var Stats
3. Calculate the standard deviation (σ) using the same method
4. For each data point, use the formula: z = (X - μ) / σ
5. Enter the calculation in the TI-84's home screen

For negative z-scores, you'll get negative results when X is less than μ.

Worked Example

Let's say you have test scores: 70, 80, 90, 100, 110. The mean (μ) is 90 and standard deviation (σ) is 15.81.

To calculate the z-score for 70:

This means 70 is 1.32 standard deviations below the mean.

Interpreting Results

Interpreting negative z-scores involves understanding their position in the distribution:

• z = -1.0: 1 standard deviation below the mean
• z = -1.5: 1.5 standard deviations below the mean
• z = -2.0: 2 standard deviations below the mean

Negative z-scores are common in:

• Statistical analysis
• Quality control
• Standardization of data
• Comparing different datasets