Examples of using Sample standard deviation in English and their translations into Greek
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Sample standard deviation.
Similarly for sample standard deviation.
This estimator is commonly used andgenerally known simply as the"sample standard deviation".
Corrected sample standard deviation.
This estimator also has a uniformly smaller mean squared error than the corrected sample standard deviation.
Which equals the sample standard deviation.
The sample standard deviation can be computed as.
If there are fewer than three data points, or the sample standard deviation is zero, SKEW.
S is the sample standard deviation. Example.
Where x and y are the sample means of X and Y, and sx andsy are the sample standard deviations of X and Y.
If omitted, the sample standard deviation is used.
See computational formula for the variance for proof, andfor an analogous result for the sample standard deviation.
This arises because the sampling distribution of the sample standard deviation follows a(scaled) chi distribution, and the correction factor is the mean of the chi distribution.
See computational formula for the variance for a proof of this fact, andfor an analogous result for the sample standard deviation.
Thus for very large sample sizes,the uncorrected sample standard deviation is generally acceptable.
This applies to both the matrix of population correlations(in which case"σ" is the population standard deviation), andto the matrix of sample correlations(in which case"σ" denotes the sample standard deviation).
This estimator, denoted by sN,is known as the uncorrected sample standard deviation, or sometimes the standard deviation of the sample(considered as the entire population), and is defined as follows.
The use of the term n- 1 is called Bessel's correction, andit is also used in sample covariance and the sample standard deviation(the square root of variance).
Similarly for sample standard deviation, s= N s 2- s 1 2 N( N- 1).{\displaystyle s={\sqrt{\frac{ Ns_{ 2}- s_{ 1}^{ 2}}{ NN-1 In a computer implementation, as the three sj sums become large, we need to consider round-off error, arithmetic overflow, and arithmetic underflow.
Such a statistic is called an estimatorand the estimator or the value of the estimator,namely the estimate is called a sample standard deviation, and is denoted by s possibly with modifiers.
When only a sample of data froma 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 a better estimate of the population standard deviation(the standard deviation of the entire population).
For example, if series of 10 measurements of previously unknown quantity is performed in laboratory,it is possible to calculate resulting sample mean and sample standard deviation, but it is impossible The mean age was 23.44 years.
If the values instead were a random sample drawn from some larger parent population, then we would have divided by 7(which is n-1) instead of 8(which is n) in the denominator of the last formula, andthen the quantity thus obtained would be called the sample standard deviation.
For example, if series of 10 measurements of previously unknown quantity is performed in laboratory,it is possible to calculate resulting sample mean and sample standard deviation, but it is impossible to calculate standard deviation of the mean.
If the values instead were a random sample drawn from some larger parent population(for example, they were 8 marks randomly chosen from a class of 20), then we would have divided by 7(which is n- 1) instead of 8(which is n) in the denominator of the last formula, andthen the quantity thus obtained would be called the sample standard deviation.
If we take a sample of n observations from a normal distribution, then the t-distribution with ν= n- 1{\displaystyle\nu =n-1} degrees of freedom can be defined as the distribution of the location of the sample mean relative to the true mean, divided by the sample standard deviation, after multiplying by the standardizing term n{\displaystyle{\sqrt{n}}}.
If the values instead were a random sample drawn from some large parent population(for example, they were 8 marks randomly and independently chosen from a class of 2 million), then one often divides by 7(which is n- 1) instead of 8(which is n) in the denominator of the last formula.In that case the result would be called the sample standard deviation.
Confidence interval of a sampled standard deviation.
The standard deviation of the sample proportions. Advertising.