Standard Deviation Calculator
Use Population σ when you have data for an entire group. Divides by N.
Frequently Asked Questions
What is the symbol for standard deviation?
The symbol for population standard deviation is σ (lowercase Greek letter sigma). For sample standard deviation, the symbol is s. In casual writing and medical journals, you will often see SD written out. In Excel, the function names use STDEV as the abbreviation.
How do you figure out standard deviation by hand?
To calculate standard deviation manually: (1) Find the mean by adding all values and dividing by the count. (2) Subtract the mean from each value, then square each result. (3) Add up all the squared values. (4) Divide by N (for population) or N−1 (for sample) to get the variance. (5) Take the square root of the variance. This gives you σ or s respectively.
How do I calculate standard deviation in Excel?
In Excel, type =STDEV(A1:A10) in any empty cell, replacing A1:A10 with your data range. This returns the sample standard deviation (divides by N−1). For population standard deviation, use =STDEVP(A1:A10) or the newer =STDEV.P(A1:A10).
What is variance vs standard deviation?
Variance (σ²) is the average of the squared differences from the mean. Standard deviation (σ) is the square root of variance. The key difference is units: if your data is in pounds (£), the variance is in pounds-squared (£²) — which is hard to interpret — while the standard deviation is back in pounds (£).
What is standard deviation in A-Level maths?
In A-Level Statistics, standard deviation measures the spread of a distribution. You use the formula σ = √(Σ(x − μ)² / N) for population SD. A-Level also covers the normal distribution N(μ, σ²), where σ directly determines the width of the bell curve. Sample SD uses N−1 as divisor (Bessel's correction).
Is a higher or lower standard deviation better?
Neither is inherently better — it depends on your goal. In quality control, a lower SD is better as it means products are consistently made to specification. In investment, a lower SD means lower risk. Context always determines whether high or low SD is desirable.