One can find the standard deviation of an entire population in cases ( such as corrected sample standard deviation " ( using " N " " 1 ), defined below, and this is often referred to as the " sample standard deviation ", without qualifiers.
32.
One can find the standard deviation of an entire population in cases ( such as corrected sample standard deviation " ( using " N " " 1 ), defined below, and this is often referred to as the " sample standard deviation ", without qualifiers.
33.
Computing a z-score requires knowing the mean and standard deviation of the complete population to which a data point belongs; if one only has a sample of observations from the population, then the analogous computation with sample mean and sample standard deviation yields the Student's t-statistic.
34.
Further, mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is ( see effect of transformations ); for example, the sample variance is an unbiased estimator for the population variance, but its square root, the sample standard deviation, is a biased estimator for the population standard deviation.
35.
The input into the normalized Gaussian function is the mean of sample means ( ~ 50 ) and the mean sample standard deviation divided by the square root of the sample size ( ~ 28.87 / } } ), which is called the standard deviation of the mean ( since it refers to the spread of sample means ) . ]]
36.
Firstly, while the sample variance ( using Bessel's correction ) is an unbiased estimate of the population variance, its square root, the sample standard deviation, is a " biased " estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen's inequality.
37.
If we take a sample of " n " observations from a normal distribution, then the " t "-distribution with \ nu = n-1 degrees of freedom can be defined as the distribution of the location of the true mean, relative to the sample mean and divided by the sample standard deviation, after multiplying by the normalizing term \ sqrt { n }.
38.
When only a sample of data from a population is available, the term "'standard deviation of the sample "'or "'sample standard deviation "'can refer to either the above-mentioned quantity as applied to those data or to a modified quantity that is an unbiased estimate of the "'population standard deviation "'( the standard deviation of the entire population ).
39.
The sample extrema can be used for a simple normality test, specifically of kurtosis : one computes the t-statistic of the sample maximum and minimum ( subtracts sample mean and divides by the sample standard deviation ), and if they are unusually large for the sample size ( as per the three sigma rule and table therein, or more precisely a Student's t-distribution ), then the kurtosis of the sample distribution deviates significantly from that of the normal distribution.
40.
Similarly, the sample variance ( estimator ), denoted " S " 2, can be used to estimate the " variance " parameter ( estimand ), denoted " ? " 2, of the population from which the sample was drawn . ( Note that the sample standard deviation ( " S " ) is not an unbiased estimate of the population standard deviation ( " ? " ) : see Unbiased estimation of standard deviation .)
