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 data points from different normal distributions.

2. How Does the Calculator Work?

The calculator uses the Z-score formula:

Where:

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

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

3. Importance of Z-Score

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

4. Using the Calculator

Tips: Enter your data value, population mean, and standard deviation. The calculator will compute how many standard deviations your value is from the mean.

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 an unusual 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, while positive scores are above the mean.

Q4: How is Z-score different from T-score?
A: Z-scores are based on population parameters (μ, σ) while T-scores are adjusted to have mean 50 and SD 10.

Q5: Where are Z-scores commonly used?
A: In standardized testing, quality control, finance (Altman Z-score), and medical measurements.