Normal and skewed distributions
A normal distribution is symmetrical, with the mean, median and mode together in the middle. In a positive skew most scores are low and a long tail stretches towards high scores, which pulls the mean up past the median; a negative skew is the mirror image. A bimodal distribution has two peaks, which often means two different groups are mixed together.
The 68, 95 and 99.7% rule
On a normal curve about 68% of scores lie within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. Everything else follows by halving and subtracting: 34% between the mean and +1, 13.5% between +1 and +2, 2.5% beyond +2. For tests of significance with these data, go to the statistical tests practice.
Questions
How do you calculate standard deviation in psychology?
Find the mean. Take it away from each score and square the answer. Add the squares, divide by N − 1 (the sample estimate) and take the square root. A bigger standard deviation means the scores are more spread out around the mean.
Where are the mean, median and mode in a skewed distribution?
The mode sits under the peak and the mean is pulled furthest towards the long tail, with the median between them. In a positive skew (tail to the right) that gives mode, median, mean from low to high; in a negative skew the order is reversed. In a normal distribution all three are about the same.
What percentage of scores lie within one standard deviation of the mean?
In a normal distribution about 68% lie within 1 standard deviation, about 95% within 2 and about 99.7% within 3. Because the curve is symmetrical, 34% lie between the mean and 1 standard deviation above it, and 16% lie beyond it.
What is percentile rank?
The percentage of scores at or below a given score. On a normal curve the mean is the 50th percentile, 1 standard deviation above it is about the 84th and 2 standard deviations above it about the 97.5th.
Should you use the mean, median or mode?
The mean uses every score, so it is the most sensitive, but one extreme score can pull it a long way. The median is better when there are outliers or skew. The mode is the only one for categories (nominal data).
Sources, checked 27 October 2026: AQA Psychology specification 7181/7182, version 1.2 (PDF), section 4.2.3.2; OCR A Level Psychology H567 specification, version 1.5 (PDF), section 1.3; AP Psychology Course and Exam Description (PDF), skills 3.B and 3.C.