Standard Deviation Calculator


Sample Standard Deviation, s15.84882762115
Variance (Sample Standard), s2251.18533696492
Population Standard Deviation, σ15.837817666628
Variance (Population Standard), σ2250.83646844136
Total Numbers, N720
Mean (Average):63.213055555556
Standard Error of the Mean (SE):0.59065093207612

Confidence Intervals Approximation, If sampling distribution of the mean follows normal distribution

Confidence LevelRange
68.3%, SE62.622404623479 - 63.803706487632
90%, 1.645SE62.24143477229 - 64.184676338821
95%, 1.960SE62.055379728686 - 64.370731382425
99%, 2.576SE61.691538754528 - 64.734572356584
99.9%, 3.291SE61.269223338093 - 65.156887773018
99.99%, 3.891SE60.914832778847 - 65.511278332264
99.999%, 4.417SE60.604150388575 - 65.821960722536
99.9999%, 4.892SE60.323591195839 - 66.102519915272

Please provide numbers separated by comma to calculate.

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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.