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 by standardizing them.

2. How Does the Calculator Work?

The calculator uses the Z-score formula:

Where:

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

Explanation: The formula subtracts the mean from the raw score and divides by the standard deviation to show how far and in what direction the value deviates from the mean.

3. Importance of Z-Score Calculation

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

4. Using the Calculator

Tips: Enter the raw value, population mean, and 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 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 type of standardized score where the mean is 50 and standard deviation is 10, commonly used in psychological testing.

Q5: Are Z-scores only for normal distributions?
A: While most meaningful for normal distributions, Z-scores can be calculated for any distribution, but interpretation differs for non-normal data.