1. What is the Z-Score?

The Z-Score measures how many standard deviations an element is from the mean. It's a dimensionless quantity used to compare 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 being measured
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula shows how far a data point is from the mean, measured in terms of standard deviations.

3. Importance of Z-Score Calculation

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

4. Using the Calculator

Tips: Enter the value you want to evaluate, the population mean, and the population 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 means 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 in a normal distribution.

Q3: Can Z-Scores be negative?
A: Yes, negative Z-Scores indicate values below the mean, while positive scores indicate values above the mean.

Q4: What's the difference between Z-Score and standard deviation?
A: Standard deviation measures dispersion in original units, while Z-Score measures distance from mean in standard deviation units.

Q5: Where are Z-Scores commonly used?
A: Z-Scores are used in quality control, finance (Altman Z-Score), medicine (growth charts), and standardized testing.