Z-Score 0.804: Complete Analysis

87.22%

Area Below

87.2

Percentile Rank

Above

Relative to Mean

Quick Interpretation

A z-score of 0.804 indicates that the value is 0.80 standard deviations above the mean. This means:

The value is relatively typical
Approximately 87.22% of values fall below this point
This score is at the 87.2 percentile

Detailed Explanation

When we say a z-score is 0.804, we're describing a point that is 0.804 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 12.1 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 72.4 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