Standard Deviation Calculator

Result

Sample Standard Deviation, s5.3763149000744
Variance (Sample Standard), s228.904761904762
Population Standard Deviation, σ4.9775003971955
Variance (Population Standard), σ224.775510204082
Total Numbers, N7
Sum:68
Mean (Average):9.7142857142857
Standard Error of the Mean (SE):2.0320560279383

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

Confidence LevelRange
68.3%, SE7.6822296863474 - 11.746341742224
90%, 1.645SE6.3715535483273 - 13.057017880244
95%, 1.960SE5.7314558995267 - 13.697115529045
99%, 2.576SE4.4797093863167 - 14.948862042255
99.9%, 3.291SE3.0267893263409 - 16.401782102231
99.99%, 3.891SE1.8075557095779 - 17.621015718994
99.999%, 4.417SE0.73869423888236 - 18.689877189689
99.9999%, 4.892SE-0.22653237438832 - 19.65510380296

Column Chart of the Values


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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.