View source for Simple random sampling

==Notations==


{| class="wikitable"
|-
!''Statistic''
!''Parametric value''
!''Sample based estimator''
|-
|Mean
|<math>\mu = \frac{\sum_{i=1}^N y_i}{N}</math>
|<math>\bar {y} = \frac{\sum_{i=1}^n y_i}{n}</math>
|-
|Variance
|<math>\sigma^2 = \frac{\sum_{i=1}^N (y_i - \mu)^2}{N}</math>
|<math>S_y^2 = \frac{\sum_{i=1}^n (y_i - \bar {y})^2}{n-1}</math>
|-
|Standard deviation
|<math>\sigma = \sqrt{\frac{\sum_{i=1}^N (y_i - \mu)^2}{N}}</math>
|<math>S_y = \sqrt{\frac{\sum_{i=1}^n (y_i - \bar {y})^2}{n-1}}</math>
|-
|Standard error
(without replacement or from a finite population)
|<math>\sigma_{\bar {y}} = \sqrt{\frac{N-n}{N-1}}*\frac {\sigma}{\sqrt{n}}</math>
|<math>S_{\bar {y}} = \sqrt{\frac{N-n}{N}}*\frac{S_y}{\sqrt{n}}</math>
|-
|Standard error
(with replacement or from an infinite population)
|<math>\sigma_{\bar {y}} = \frac{\sigma}{\sqrt{n}}</math>
|<math>S_{\bar {y}} = \frac{S_y}{\sqrt{n}}</math>
|}


Where,
{|
|-
| <math>N \!</math> || number of sampling elements in the population (= population size);
|-
| <math>n \!</math> || number of sampling elements in the sample (= sample size);
|-
| <math>y_i \!</math> || observed value of i-th sampling element;
|-
| <math>\mu \!</math> || parametric mean of the population;
|-
| <math>\bar {y} </math> || estimated mean;
|-
| <math>\sigma \!</math> || standard deviation in the population;
|-
| <math>S \!</math> || estimated standard deviation in the population;
|-
| <math>\sigma^2 \!</math> || parametric variance in the population;
|-
| <math>s^2 \!</math> || estimated variance in the population;
|-
| <math>\sigma_{\bar {y}} </math> || parametric standard error of the mean;
|-
| <math>s_{\bar {y}} </math> || estimated standard error of the mean.
|}



{{Exercise
|message=Simple random sampling examples
|alttext=test
|text=2 exercises for this topic
}}