1. What is a Z-Score Calculator?

Definition: This calculator computes the standard score (z-score) which represents how many standard deviations a data point is from the mean.

Purpose: It helps in statistical analysis to understand where a particular data point lies in relation to the distribution's mean.

2. How Does the Z-Score Calculator Work?

The calculator uses the formula:

Where:

• \( z \) — Z-score (dimensionless)
• \( x \) — Data point (context-specific units)
• \( \mu \) — Mean of the distribution (same units as x)
• \( \sigma \) — Standard deviation (same units as x)

Explanation: The difference between the data point and mean is divided by the standard deviation to normalize the value.

3. Importance of Z-Score Calculation

Details: Z-scores allow comparison of data points from different normal distributions and help identify outliers.

4. Using the Calculator

Tips: Enter the data point 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 data point is exactly at the mean.

Q2: What's 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 relationship between z-scores and percentiles?
A: Z-scores can be converted to percentiles using standard normal distribution tables.

Q5: When would I use this calculator?
A: Useful for statistics, quality control, psychology testing, and any field using standardized measurements.