1. What is 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:

• \( z \) — Z-score (dimensionless)
• \( x \) — Value being standardized
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula shows how far a value deviates from the mean in units of standard deviation.

3. Importance of Z-score

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

4. Using the Calculator

Tips: Enter the value (x), population mean (μ), and population standard deviation (σ). 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 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.

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 adjusted Z-scores with a mean of 50 and standard deviation of 10, commonly used in bone density measurements.

Q5: Where are Z-scores commonly used?
A: In standardized testing, quality control, finance, medical measurements, and any field requiring standardization of measurements.