Z-Score Explained: Understanding Data Relative to the Mean
Student Question
What is z-score?
Solution
-
Step 1: To understand what a z-score is, it's important to know that it is a statistical measurement describing a value's relationship to the mean of a group of values.
-
Step 2: The z-score is calculated using the formula: $$ z = \frac{(X - \mu)}{\sigma} $$ where ( X ) is the value being measured, ( \mu ) is the mean of the data set, and ( \sigma ) is the standard deviation of the data set.
-
Step 3: A z-score tells us how many standard deviations away from the mean the value ( X ) is. If the z-score is 0, it means ( X ) is exactly at the mean. A positive z-score indicates ( X ) is above the mean, while a negative z-score indicates ( X ) is below the mean.
Answer
The z-score is a measure of how many standard deviations a data point is from the mean.
Key Concept
Z-score
Explanation
A z-score quantifies the number of standard deviations a data point is from the mean of its data set.
