1. What Is The Z-Score?

The Z-score, also known as the standard score, measures how many standard deviations an element is from the mean. It is a key concept in statistics and normal distribution analysis.

2. How Does The Calculator Work?

The calculator uses the Z-score formula:

Where:

• \( Z \) — Z-score (standard score)
• \( x \) — Individual data point value
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula calculates how many standard deviations a particular value is above or below the mean of the distribution.

3. Importance Of Z-Score Calculation

Details: Z-scores are essential for comparing data points from different normal distributions, identifying outliers, and calculating probabilities in standard normal distribution tables.

4. Using The Calculator

Tips: Enter the value (x), population mean (μ), and standard deviation (σ). Standard deviation must be greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive Z-score indicate?
A: A positive Z-score indicates the data point is above the mean of the distribution.

Q2: What does a negative Z-score indicate?
A: A negative Z-score indicates the data point is below the mean of the distribution.

Q3: What is considered a significant Z-score?
A: Typically, Z-scores beyond ±2 are considered unusual, and beyond ±3 are considered outliers in a normal distribution.

Q4: Can Z-scores be used for non-normal distributions?
A: While Z-scores can be calculated for any distribution, their interpretation is most meaningful for normal distributions.

Q5: How are Z-scores related to probability?
A: Z-scores can be converted to probabilities using standard normal distribution tables, showing the likelihood of a value occurring within the distribution.