Z-Score 20: Complete Analysis

100.00%
Area Below
100.0
Percentile Rank
Above
Relative to Mean

Quick Interpretation

A z-score of 20 indicates that the value is 20.00 standard deviations above the mean. This means:

  • The value is quite unusual
  • Approximately 100.00% of values fall below this point
  • This score is at the 100.0 percentile

Detailed Explanation

When we say a z-score is 20, we're describing a point that is 20.000 standard deviations above the mean of a normal distribution. This helps us understand how unusual or common a value is compared to the average.

Real-World Examples

Example 1: Test Scores
If this z-score represented a test score, it would mean the student scored above average by 300.0 points (assuming a standard deviation of 15 points).
Example 2: Height
For adult male height (mean ≈ 5'10", SD ≈ 3"), this z-score would represent someone who is approximately 130.0 inches tall.

Common Uses

Field Application
Education Standardized test scores, grade distributions
Psychology IQ scores, personality assessments
Medicine Growth charts, lab results
Quality Control Manufacturing specifications, process control

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