Sample or population — this changes your answer
The only difference between the two formulas is the divisor: population variance divides by n, sample variance by n−1. That subtraction is Bessel's correction, and it exists because a sample's own mean sits closer to the sample than the true population mean does, which makes the deviations systematically too small. Dividing by the smaller number compensates.
Practically: if your numbers are the whole group you care about — every student in one class, every machine on one line — use population. If they are a sample you are generalising from, use sample. When in doubt, use sample; it is the default in most software and every statistics course.
Reading the result
Standard deviation is in the same units as your data, which makes it directly interpretable: a mean of 70 with an SD of 10 means most values sit roughly between 60 and 80. Variance is the same information squared, so it is mathematically convenient but not intuitive — you cannot describe it in the original units.
For roughly bell-shaped data, about 68% of values fall within one SD of the mean, 95% within two, and 99.7% within three.
Frequently asked questions
Why is my sample SD larger than the population SD?
Because it divides by a smaller number (n−1 rather than n). The gap shrinks as the sample grows — at n=100 the difference is under 1%, at n=5 it is substantial.
Can I rely on this for coursework or research?
Results are checked against published worked examples. Sample and population versions differ by whether you divide by n-1 or n; both are shown, because courses differ.
Is my data uploaded?
No. Your data set is never transmitted, which matters when it is unpublished research.
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