1. What is a Z-Score?

A Z-Score (standard score) measures how many standard deviations an element is from the mean. It allows comparison of scores from different normal distributions.

2. How Does the Calculator Work?

The calculator uses the Z-Score formula:

Where:

• \( Z \) — Z-Score (dimensionless)
• \( x \) — Raw score/value
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula shows how far a data point is from the mean in terms of standard deviations.

3. Importance of Z-Score

Details: Z-Scores are crucial in statistics for comparing different data points within and between datasets, identifying outliers, and standardizing scores.

4. Using the Calculator

Tips: Enter the raw 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, often used in psychological testing.

Q5: When shouldn't I use Z-Scores?
A: Z-Scores assume normal distribution and aren't appropriate for highly skewed data without transformation.