1. What is the Z-Score Formula?

The Z-Score formula measures how many standard deviations a data point (x) is from the mean (μ) of a distribution. It standardizes data to allow comparison across different datasets and identifies outliers in statistical analysis.

2. How Does the Calculator Work?

The calculator uses the standard Z-Score formula:

Where:

• \( z \) — Z-Score (unitless)
• \( x \) — Raw score (unitless)
• \( \mu \) — Mean of the population (unitless)
• \( \sigma \) — Standard deviation of the population (unitless)

Explanation: The formula calculates the number of standard deviations a particular data point is above or below the population mean.

3. Importance of Z-Score Calculation

Details: Z-Scores are crucial for standardizing data, identifying outliers, comparing results from different normal distributions, and calculating probabilities in statistics and research.

4. Using the Calculator

Tips: Enter the raw score (x), population mean (μ), and standard deviation (σ). Standard deviation must be greater than zero. All values are unitless.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive/negative z-score indicate?
A: A positive z-score indicates the data point is above the mean, while a negative z-score indicates it's below the mean.

Q2: What is considered a significant z-score?
A: Typically, z-scores beyond ±2 are considered unusual, and beyond ±3 are considered outliers in a normal distribution.

Q3: Can z-scores be used for non-normal distributions?
A: While z-scores can be calculated for any distribution, their interpretation is most meaningful for normal distributions.

Q4: How are z-scores related to probability?
A: Z-scores can be converted to probabilities using the standard normal distribution table or statistical software.

Q5: What's the difference between z-score and t-score?
A: Z-scores are used when population parameters are known, while t-scores are used when working with sample data and estimating population parameters.