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

Explanation: The formula shows how far a data point is 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 for analysis.

4. Using the Calculator

Tips: Enter the value you want to analyze, the population mean, and the standard deviation. 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 means 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 in a normal distribution.

Q3: Can Z-Scores be negative?
A: Yes, negative Z-Scores indicate values below the mean, while positive scores are above 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 educational testing.

Q5: When shouldn't I use Z-Scores?
A: Z-Scores assume normal distribution. They may be misleading with highly skewed distributions or small sample sizes.