A negative z-score means a value falls below the average. Specifically, it tells you how far below: a z-score of -1 means the value is exactly one standard deviation below the mean, while a z-score of -2 means it’s two standard deviations below. The negative sign is the key piece of information, instantly telling you which side of the average you’re on.
How the Negative Sign Appears
A z-score is calculated by taking your value, subtracting the mean, and dividing by the standard deviation. When your value is smaller than the mean, that subtraction produces a negative number. That’s all the negative sign represents: your raw number was less than the group average.
For example, if the average IQ score is 100 with a standard deviation of 15, and someone scores 85, the z-score is (85 – 100) / 15 = -1.0. That person scored exactly one standard deviation below the mean. If someone else scored 115, their z-score would be +1.0, one standard deviation above. The sign flips depending on which side of the average you land.
Where It Sits on the Bell Curve
On a standard bell curve, the mean sits right in the center with a z-score of 0. Positive z-scores stretch to the right, and negative z-scores stretch to the left. The further negative the z-score, the further left you move into the tail of the distribution, where fewer and fewer values exist.
Standard normal distribution tables quantify exactly how rare a given z-score is by showing the percentage of values that fall to its left. A z-score of -1.0 has about 15.9% of all values below it, meaning roughly 84% of the population scored higher. A z-score of -2.0 drops to just 2.3% below it. By the time you reach -3.0, only about 0.13% of values fall that low. So a mildly negative z-score (like -0.5) is completely ordinary, while a very negative one (like -3.0) is genuinely rare.
Quick Reference for Common Z-Scores
- Z = -0.5: Slightly below average. About 31% of values fall below this point.
- Z = -1.0: One standard deviation below the mean. About 16% fall below.
- Z = -1.5: About 6.7% fall below.
- Z = -2.0: Two standard deviations below the mean. Only about 2.3% fall below.
- Z = -3.0: Extremely low. Only about 0.1% fall below.
Negative Z-Scores on Standardized Tests
If you’re looking at test results, a negative z-score simply means you scored below the average of everyone who took the test. A z-score of -1.4, for instance, means you performed 1.4 standard deviations below the mean. In practical terms, that means you scored as well as or better than only about 8% of test-takers.
Many testing systems actually convert z-scores into other scales partly to avoid negative numbers, since people find them discouraging. The SAT, for example, uses a scaled score with a mean of 1000, so even below-average performers see a positive number. IQ tests use a mean of 100 and a standard deviation of 15. An IQ of 95 corresponds to a z-score of -0.33, which is barely below average and well within the normal range.
Negative Z-Scores in Health and Growth Charts
Pediatricians use z-scores to track whether a child’s weight and height are on track compared to global growth standards set by the World Health Organization. Here, negative z-scores carry specific clinical meaning.
A child whose weight-for-height falls below -2 standard deviations is classified as wasted (acutely malnourished). Below -3 standard deviations meets the threshold for severe acute malnutrition, a condition where the risk of death is more than nine times higher than for children above -1. These cutoffs illustrate how negative z-scores can shift from “slightly below average” to “medically urgent” depending on how far they fall from zero.
Negative Z-Scores in Statistical Testing
In statistics classes or research contexts, negative z-scores also appear when testing hypotheses. Certain critical z-values act as boundaries for deciding whether a result is statistically significant. For a two-tailed test at the 95% confidence level, the critical values are -1.96 and +1.96. Any z-score more extreme than -1.96 (further into the left tail) is considered statistically significant at that level. At 99% confidence, the threshold moves to -2.58.
These thresholds are symmetric. A z-score of -1.96 is just as statistically significant as +1.96. The negative version simply means the observed value was significantly lower than expected, rather than significantly higher.
Negative Does Not Mean Bad
A negative z-score is not inherently good or bad. It depends entirely on what’s being measured. If you’re measuring cholesterol, a negative z-score means your level is below average, which is generally favorable. If you’re measuring income, it means you earn less than the mean. For a child’s growth, a mildly negative z-score (like -0.5) is perfectly healthy.
The z-score is just a ruler. It tells you how far and in which direction a value sits relative to the group average. The negative sign means “below the mean,” and the number tells you how far below, measured in standard deviations. A value near zero is close to typical, and the further the z-score drifts from zero in either direction, the more unusual it becomes.