1. What is a Z-Score?

A Z-score (standard score) measures how many standard deviations a data point is from the mean of a distribution. It allows comparison of values from different normal distributions by standardizing them.

2. How Does the Calculator Work?

The calculator uses the Z-score formula:

Where:

• \( x \) — The data point being evaluated
• \( \text{Mean} \) — The mean of the population
• \( \text{SD} \) — The standard deviation of the population

Explanation: The formula subtracts the mean from the data point to get the deviation from the mean, then divides by the standard deviation to express this deviation in standard deviation units.

3. Importance of Z-Score Calculation

Details: Z-scores are essential in statistics for comparing different data sets, identifying outliers, and performing hypothesis testing. They are widely used in psychology, education, medicine, and quality control.

4. Using the Calculator

Tips: Enter the data point value, population mean, and standard deviation. The standard deviation must be greater than zero. The calculator will compute how many standard deviations your data point is from the mean.

5. Frequently Asked Questions (FAQ)

Q1: What does a Z-score of 0 mean?
A: A Z-score of 0 means the data point 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's the difference between Z-score and T-score?
A: T-scores are a type of standardized score with a mean of 50 and SD of 10, while Z-scores have mean 0 and SD 1.

Q5: When can't I use Z-scores?
A: Z-scores assume normal distribution and shouldn't be used with highly skewed data without transformation.