GlenCalc

Standard deviation calculator

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Your answer

Sample standard deviation (s)2.748737
Variance7.555556
Mean15
Count10
Sum150
Standard error of the mean0.869227
Quartiles (Q1, median, Q3)13, 15, 17
Minimum, maximum11, 20
Deviations from the mean
xx − mean(x − mean)²
12-39
1500
11-416
1839
1500
20525
14-11
1500
13-24
1724

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How we worked it out

Updated as you change the numbers.

  1. Mean = 150 ÷ 10 = 15.
  2. Sum of squared deviations = 68.
  3. Variance = 68 ÷ (10 − 1) = 7.555556.
  4. Standard deviation = √variance = 2.748737.

Method and assumptions

Standard deviation measures how spread out values are around the mean: the square root of the average squared deviation. A sample divides by n − 1 (Bessel’s correction) because a sample’s own mean sits closer to its values than the true mean does. Quartiles use the median-of-halves method.

Questions

What is the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9?

2 as a population, or about 2.14 as a sample.

Sources

Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.

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