1. What is the Normality of Distribution?

The Z-score measures how many standard deviations an element is from the mean. It's used to assess normality in statistical distributions and identify outliers.

2. How Does the Calculator Work?

The calculator uses the Z-score formula:

Where:

• \( x \) — Individual value
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: A Z-score of 0 indicates the value is identical to the mean. Positive Z-scores indicate values above the mean, negative scores indicate values below the mean.

3. Importance of Z-Score Calculation

Details: Z-scores are crucial for determining how unusual a value is within a distribution, comparing values from different normal distributions, and identifying outliers.

4. Using the Calculator

Tips: Enter the 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 1.0 mean?
A: A Z-score of 1.0 means the value is 1 standard deviation above the mean.

Q2: What range of Z-scores is considered normal?
A: Typically, Z-scores between -2 and +2 are considered within the normal range (covering about 95% of values in a normal distribution).

Q3: Can Z-scores be used with non-normal distributions?
A: While possible, interpretation is less straightforward as the properties of normal distribution don't apply.

Q4: How is Z-score different from standard deviation?
A: Standard deviation is a measure of dispersion, while Z-score measures how many standard deviations a particular value is from the mean.

Q5: What's considered an extreme Z-score?
A: Typically, Z-scores beyond ±3 are considered extreme (occurring in about 0.3% of cases in a normal distribution).