1. What is a Z-Score?

A Z-score measures how many standard deviations an element is from the mean. It's a dimensionless quantity used to compare data points from different normal distributions.

2. How Does the Calculator Work?

The calculator uses the Z-Score formula:

Where:

• \( x \) — The value to be standardized
• \( \mu \) — The mean of the population
• \( \sigma \) — The standard deviation of the population

Explanation: The formula shows how many standard deviations a value (x) is above or below the population mean (μ).

3. Importance of Z-Score Calculation

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

4. Using the Calculator

Tips: Enter the raw value, population mean, and 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 at 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: What's the difference between Z-score and T-score?
A: T-scores are a type of standardized score where the mean is 50 and standard deviation is 10, while Z-scores have mean 0 and SD 1.

Q5: When should I use Z-scores?
A: Use them when you need to compare measurements from different scales or determine how unusual a value is within its distribution.