1. What is the 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 by standardizing them.

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 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 standardize, 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 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 in a normal distribution.

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

Q4: What are common uses of Z-Scores?
A: Used in standardized testing, quality control, finance (Altman Z-Score), and medical/anthropometric measurements.

Q5: 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 bone density measurements.