1. What is the Z Score?

The Z score (standard score) indicates how many standard deviations an element is from the mean. It's a dimensionless quantity used to compare different data points within a normal distribution.

2. How Does the Calculator Work?

The calculator uses the Z score formula:

Where:

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

Explanation: The formula measures the distance between a data point and the population mean in terms of standard deviations.

3. Importance of Z Score

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

4. Using the Calculator

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

Q4: What's the difference between Z score and T score?
A: T scores are a transformation of Z scores with a mean of 50 and standard deviation of 10, often used in psychological testing.

Q5: When should I use Z scores?
A: Use Z scores when you need to compare data points from different normal distributions or identify how unusual a value is within its distribution.