1. What is a Z-score Calculator?

Definition: This calculator computes the standard score (z-score) which indicates how many standard deviations an element is from the mean.

Purpose: It helps in statistical analysis to compare different data points across various normal distributions.

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 (same units as x)
• \( \sigma \) — Standard deviation (same units as x)

Explanation: The z-score measures the distance between a data point and the population mean in units of standard deviation.

3. Importance of Z-score Calculation

Details: Z-scores enable comparison of values from different normal distributions and are fundamental in hypothesis testing, quality control, and probability calculations.

4. Using the Calculator

Tips: Enter your data point (x), population mean (μ), and standard deviation (σ). Standard deviation must be > 0.

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 rare in normal distributions.

Q3: Can z-scores be negative?
A: Yes, negative z-scores indicate values below the mean.

Q4: When would I use a z-score?
A: When you need to standardize data for comparison, calculate probabilities, or perform statistical tests.

Q5: What's the relationship between z-scores and percentiles?
A: Z-scores can be converted to percentiles using standard normal distribution tables or functions.