1. What is a Z-Score Calculator?

Definition: This calculator computes the standard score (z-score) which measures 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.

2. How Does the Z-Score Calculator Work?

The calculator uses the formula:

Where:

• \( z \) — Z-score (standard score)
• \( x \) — Raw data point being measured
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

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

3. Importance of Z-Score Calculation

Details: Z-scores are fundamental in statistics for comparing different data points across different normal distributions, identifying outliers, and calculating probabilities.

4. Using the Calculator

Tips: Enter the data point value, population mean, and population standard deviation. Standard deviation must be greater than 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 of the distribution.

Q2: What's considered a "significant" z-score?
A: Typically, z-scores beyond ±2 are considered unusual, and beyond ±3 are very rare 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: How is this different from a t-score?
A: Z-scores are used when population parameters are known, while t-scores are used with sample statistics.

Q5: What units does the z-score have?
A: Z-scores are dimensionless - they represent the number of standard deviations from the mean.