Standard Deviation Calculator

Result

Sample Standard Deviation, s15.84882762115
Variance (Sample Standard), s2251.18533696492
Population Standard Deviation, σ15.837817666628
Variance (Population Standard), σ2250.83646844136
Total Numbers, N720
Sum:45513.4
Mean (Average):63.213055555556

Confidence Intervals, If Normal Distribution

Confidence LevelRange
68.3%, σ47.364227934406 - 79.061883176705
90%, 1.645σ37.141734118764 - 89.284376992347
95%, 1.960σ32.149353418102 - 94.276757693009
99%, 2.576σ22.386475603474 - 104.03963550764
99.9%, 3.291σ11.054563854352 - 115.37154725676
99.99%, 3.891σ1.5452672816618 - 124.88084382945
99.999%, 4.417σ-6.791216047063 - 133.21732715817
99.9999%, 4.892σ-14.319409167109 - 140.74552027822

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Standard Deviation

The following is the definition of the standard definition σ, also called population standard deviation if the entire population can be measured, where µ is the expectation, xi is one sample value, and N is the total number of samples. σ2 is called variance.

One can find the standard deviation of an entire population in cases where every member of a population is sampled. In most cases, this cannot be done. The standard deviation σ is estimated by examining a random sample taken from the population.

Sample Standard Deviation

The most common estimator for σ used is an adjusted version, the sample standard deviation, denoted by "s" and defined as follows. s2 is the sample standard variance.