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.

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 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?

So a value at mean + 1 SD sits at about the 84th percentile: 84.13% of a normal distribution lies below it and 15.87% above it. Those are normal-model shares computed from the standard normal CDF, not counts from any data set. In the table σ means the standard deviation of the normal model; when you work from your own data, use your sample SD (s) or population SD in its place.

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

Quiz scores (illustrative): 62, 67, 70, 71, 73, 75, 76, 78, 79, 80, 82, 84, 86, 89, 93

Sample vs Population SD Changes the Cutoff

The same 15 scores give two different cutoffs. With the population formula the cutoff drops to 85.80, so 86 moves above it, while the sample cutoff 86.09 leaves it below. Use the sample formula when the scores are a sample of a larger group and the population formula when they are the whole group you care about, and state which one you used whenever a score sits close to the line.

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.

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.

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.

Related: How to Interpret Standard Deviation, Z-Score Explained and Standard Deviation and Normal Distribution.