Z-Scores and Standardization

Statistics · Axiom Academy

LESSON Z-Scores and Standardization Learn how to convert values to z-scores and interpret their meaning in a distribution The z-score formula standardizes any value by measuring its distance from the mean in units of standard deviation: z = the z-score (number of standard deviations from the mean) x = the raw value we're converting σ (sigma) = the population standard deviation 2. Computing a Z-Score: Example Let's calculate the z-score for a specific value. Suppose test scores have a mean (μ) of 75 and standard deviation (σ) of 10. What is the z-score for a student who scored 90? Z-scores provide a standardized way to understand where values fall in a distribution: z = 0: Value equals the mean (average) z = 1: One standard deviation above the mean z = -1: One standard deviation below the mean z = 2: Two standard deviations above (unusual) z > 3 or z Extremely unusual values (outliers) Z-scores are powerful tools used across many fields: Education: Comparing test scores across different exams or classes Medicine: Identifying abnormal blood test results or growth patterns Quality Control: Detecting defective products in manufacturing Finance: Assessing risk and identifying unusual market movements Sports: Comparing athlete performance across different metrics

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