1. What is a Z Score?

A Z-score (standard score) measures how many standard deviations an element is from the mean. It's used in hypothesis testing, quality control, and comparing results from different normal distributions.

2. How Does the Calculator Work?

The calculator uses the Z Score formula:

Where:

• \( x \) — Raw data point
• \( \text{Mean} \) — Mean of the population
• \( \text{Standard Deviation} \) — Standard deviation of the population

Explanation: The formula standardizes different data points to make them comparable across different scales and distributions.

3. Importance of Z Scores

Details: Z scores are fundamental in statistics for determining how unusual a value is within a distribution, calculating probabilities, and making statistical inferences.

4. Using the Calculator

Tips: Enter the raw data point, population mean, and population 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 means the data point is exactly at the mean of the distribution.

Q2: What is considered a significant Z score?
A: Typically, Z scores beyond ±1.96 are considered statistically significant at the 5% level (two-tailed test).

Q3: Can Z scores be negative?
A: Yes, negative Z scores indicate values below the mean, while positive scores indicate values above the mean.

Q4: How is Z score different from T score?
A: Z scores are based on population parameters (known mean and SD), while T scores are used when working with sample data and estimating population parameters.

Q5: What's the relationship between Z scores and p-values?
A: Z scores can be converted to p-values using the standard normal distribution table, indicating the probability of observing such an extreme value.