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:

• \( Z \) — 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 terms of standard deviation units.

3. Importance of Z-Score Calculation

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

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.

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 transformation of Z-Scores with mean 50 and standard deviation 10, commonly used in educational testing.

Q5: When shouldn't Z-Scores be used?
A: Z-Scores assume normal distribution and shouldn't be used with highly skewed data without appropriate transformations.