1. What is a Z-Score?

The 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:

• \( x \) — The value being measured
• \( \mu \) — The mean of the population
• \( \sigma \) — The standard deviation of the population

Explanation: The Z-Score indicates how far and in what direction a value deviates from the mean, measured in standard deviations.

3. Importance of Z-Score

Details: Z-Scores are crucial in statistics for comparing different data points across different distributions, identifying outliers, and standardizing scores for comparison.

4. Using the Calculator

Tips: Enter the value you want to analyze, the population mean, and the population 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 indicates the value is exactly equal to the mean.

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: How is Z-Score different from T-Score?
A: T-Scores are a type of standardized score with a mean of 50 and standard deviation of 10, while Z-Scores use mean 0 and SD 1.

Q5: Where are Z-Scores commonly used?
A: In quality control, finance (Altman Z-Score), standardized testing, and scientific research.