Calculate the z-score of a value given a mean and standard deviation.
Frequently Asked Questions (FAQs):
- What is a Z-score, and why is it important?
- A Z-score, also known as a standard score, measures how many standard deviations a data point is away from the mean of a distribution. It's crucial in statistics for comparing and standardizing different data points, regardless of their original units.
- What is the formula for calculating the Z-score?
- The formula for calculating the Z-score for a data point x, given the mean μ and the standard deviation σ, is:
- Where x is the data point, μ is the mean, and σ is the standard deviation.
- How do I interpret Z-score values?
- Positive Z-scores indicate that the data point is above the mean, while negative Z-scores indicate it's below the mean. A Z-score of 0 means the data point is equal to the mean. The magnitude of the Z-score shows how far the data point deviates from the mean in terms of standard deviations.