1. What is the Z-Score?

The Z-Score (standard score) measures how many standard deviations an element is from the mean. It's a dimensionless quantity used to compare different normal distributions.

2. How Does the Calculator Work?

The calculator uses the Z-Score formula:

Where:

• \( Z \) — Z-Score (dimensionless)
• \( x \) — Value being measured
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula shows how far a data point deviates from the mean, measured in standard deviation units.

3. Importance of Z-Score

Details: Z-Scores are crucial in statistics for comparing values from different normal distributions, identifying outliers, and standardizing scores.

4. Using the Calculator

Tips: Enter the value (x), population mean (μ), and population standard deviation (σ). Standard deviation must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a Z-Score of 0 mean?
A: A Z-Score of 0 indicates the value is exactly at the mean of the distribution.

Q2: What is considered a "high" Z-Score?
A: Typically, Z-Scores beyond ±2 are considered unusual, and beyond ±3 are very unusual.

Q3: Can Z-Scores be negative?
A: Yes, negative Z-Scores indicate values below the mean.

Q4: What's the difference between Z-Score and T-Score?
A: T-Scores are a transformation of Z-Scores with mean 50 and standard deviation 10, commonly used in educational testing.

Q5: How are Z-Scores used in real life?
A: They're used in quality control, finance (altman Z-score), standardized testing, and medical measurements.