One Standard Deviation Above the Mean: Meaning and Example

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

Cutoff = mean + SD. z = +1. Normal-model percentile ≈ 84.13 (15.87% above). The arithmetic is always valid; the percentile applies only when the data are roughly symmetric and single-peaked.

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

cutoff = mean + SD

Equivalent z-score

z = (x − mean) / SD = 1

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?

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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

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Sample vs Population SD Changes the Cutoff

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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.

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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

For right-skewed data such as waiting times or incomes, the share above mean + 1 SD can differ a lot from 15.87%, and mean − 1 SD can even be impossible (below zero). Use percentiles or the IQR instead; see Interquartile Range vs Standard Deviation.

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

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How to Read This Article

A statistics tutorial is a practical interpretation guide, not just a formula dump. It refers to the assumptions, notation, and reporting language that analysts need when they explain a result to a teacher, manager, client, or reviewer. The article body covers the specific topic, while the sections below create a common interpretation frame that readers can reuse across related metrics.

Reading goal	What to focus on	Common mistake
Definition	What the metric is and what quantity it summarizes	Treating the formula as self-explanatory
Formula choice	Sample versus population assumptions and notation	Using n when n-1 is required or vice versa
Interpretation	Whether the result indicates concentration, spread, or risk	Calling a large value good or bad without context

Frequently Asked Questions

What percentile is one standard deviation above the mean?

On a normal distribution, about the 84th percentile: 84.13% of values are below mean + 1 SD and 15.87% are above it. In real data the share can differ, so count it if you have the raw values.

What percent of data is between the mean and one standard deviation above it?

About 34.13% on a normal distribution. Together with the matching 34.13% below the mean, that makes the 68.27% within ±1 SD.

Is one standard deviation above the mean good?

It means above average by one typical spread. For a score where higher is better, that is a strong result; for a measure where lower is better, such as defects or delays, it is a warning. It is not an outlier on its own.

How do you calculate one standard deviation above the mean?

Add the standard deviation to the mean. With a mean of 77.67 and a sample SD of 8.42, the cutoff is 86.09.

What is one standard deviation below the mean?

Mean − SD, a z-score of −1, about the 16th percentile on a normal distribution. For IQ (mean 100, SD 15) it is 85.

Authoritative References

These sources define the concepts referenced most often across our articles. Bessel's correction is a sample adjustment, variance is a squared measure of spread, and standard deviation is the square root of variance expressed in the same units as the data.