GRE Standard Deviation & the Normal Distribution
Standard deviation measures one thing: how spread out a set of numbers is around its mean. The GRE rarely asks you to compute it by hand; it wants to know if you understand it. Drag the tool below to see how the mean and the spread reshape the bell curve.
Spread around the mean
A small standard deviation means the values huddle close to the mean; a large one means they scatter. The normal distribution, the bell curve, is the shape the GRE builds most statistics questions around. Move the mean and the spread and watch how the curve slides and widens.
The normal curve
In a normal (bell-shaped) distribution, about what share of values land within one standard deviation of the mean?
The empirical rule (68-95-99.7)
For a normal distribution, the percentages are fixed and worth memorizing:
- About 68% of values fall within 1 standard deviation of the mean.
- About 95% fall within 2 standard deviations.
- About 99.7% fall within 3 standard deviations.
The curve is symmetric, so half of the remaining tail sits on each side. That one fact answers most GRE normal-distribution questions.
The behavior rules
- Add a constant to every value: mean shifts, standard deviation is unchanged.
- Multiply every value by a constant: standard deviation scales by that constant.
- Tighter cluster: smaller standard deviation. Two sets can share a mean and have very different spreads.
Frequently asked questions
Do you have to calculate standard deviation on the GRE?
Almost never by hand. The GRE tests whether you understand what standard deviation means, spread around the mean, and how it behaves. It far more often asks you to compare two data sets or reason with the normal distribution than to compute a raw value.
What is the 68-95-99.7 rule?
For a normal distribution, about 68% of values fall within 1 standard deviation of the mean, about 95% within 2, and about 99.7% within 3. This empirical rule is the single most testable fact about the bell curve on the GRE.
What changes the standard deviation of a data set?
Adding the same constant to every value shifts the mean but leaves the standard deviation unchanged. Multiplying every value by a constant scales the standard deviation by that constant. A tighter cluster of values means a smaller standard deviation.
Standard deviation vs. variance, what is the difference?
Variance is the average of the squared distances from the mean; standard deviation is the square root of the variance. Standard deviation is in the same units as the data, which is why it is the more intuitive measure of spread.
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