What Is One Standard Deviation Above the Mean?
One standard deviation above the mean is the single value mean + standard deviation, which has a z-score of +1. On a normal (bell-shaped) distribution it sits at about the 84th percentile: 84.13% of values are below it and 15.87% are above it. For example, IQ tests are scaled to a mean of 100 and a standard deviation of 15, so one SD above the mean is 100 + 15 = 115.
Key result
To find it from raw data, paste your numbers into the standard deviation calculator: the ±1/2/3 SD limits panel shows mean + 1 SD directly. The worked example below opens with the data already loaded.
Formula, Z-Score and Quick Examples (IQ, Test Scores)
One standard deviation above the mean
Equivalent z-score
| Mean | SD | One SD above | One SD below | Two SDs above |
|---|---|---|---|---|
| 100 (IQ scale) | 15 | 115 | 85 | 130 |
| 72 | 8 | 80 | 64 | 88 |
| 10 | 3 | 13 | 7 | 16 |
One SD above the mean is a single number, not a range: with a mean of 10 and an SD of 3 it is 13. "Within one SD" is the range from mean − SD to mean + SD (7 to 13). If you already know the mean, SD and a raw value, the z-score calculator gives how many SDs above the mean that value is.
What Percent of Data Is Above One Standard Deviation?
@@osd-percent@@
The often-quoted 34% is the slice between the mean and +1 SD (34.13%). Half of the 68% that lies within ±1 SD sits on each side of the mean, and the 50% below the mean plus 34.13% gives 84.13% below mean + 1 SD, which is the 84th percentile.
Worked Example: Find the Cutoff in Your Own Data
@@osd-example@@
Sample vs Population SD Changes the Cutoff
@@osd-modes@@
One SD Above the Mean on a Bell Curve
On a bell curve the mean is the peak and one SD above it is one marked step to the right, where the curve switches from curving down to curving up (its inflection point). The chart uses the mean and sample SD of the quiz scores, with markers at the mean, mean + 1 SD and mean + 2 SD.
@@osd-chart@@
The Empirical Rule extends the same picture: about 68% within ±1 SD, 95% within ±2 SD and 99.7% within ±3 SD, again only for roughly normal data.
Is One SD Above the Mean Good, Unusual or an Outlier?
Above average, yes; unusual, usually not. On a normal model about 1 in 6 values (15.87%) is above +1 SD, so a value there is common. Common outlier screens start much further out, at |z| > 2 or |z| > 3; see Outlier Detection.
| Position | z | Normal share above | Typical reading |
|---|---|---|---|
| Mean + 1 SD | +1 | 15.87% | Above average, common |
| Mean + 2 SD | +2 | 2.28% | Unusually high |
| Mean + 3 SD | +3 | 0.13% | Rare; check for errors or a different process |
Whether "one SD above" is good depends on the measure: one SD above the mean on a test score is a strong result, while one SD above the mean on defect rate or response time is a warning sign.
Checklist Before You Use the Cutoff
- Compute the mean and SD from the same data set, time window, group and unit.
- Say whether you used the sample (n − 1) or population (n) formula; review Sample vs Population if a value sits near the cutoff.
- Check the shape before quoting the 84th percentile. Skewed or two-peaked data can put far more or far fewer values above +1 SD.
- Look for extreme values first: one bad data point inflates the SD and moves the cutoff up.
- Report the count above the cutoff from your data alongside any normal-model percentage.
When the 84th percentile is wrong
Related: How to Interpret Standard Deviation, Z-Score Explained and Standard Deviation and Normal Distribution.
Further Reading
Sources
References and further authoritative reading used in preparing this article.
- NIST/SEMATECH e-Handbook of Statistical Methods: What do we mean by Normal data? — National Institute of Standards and Technology
- Introductory Statistics 2e: The Normal Distribution — OpenStax