6.13
Consider spinning ten picker wheels and finding the mean of outcomes. This process is repeated, say 20,000 times.
The sample mean obtained for each repetition of the process is plotted, which looks similar to a normal distribution graph.
If the sample size is large, the distribution gets closer to the normal distribution, and the mean of the sample means gets closer to the population mean.
Such distribution of values of a statistic such as mean, variance, or a sample proportion is known as the sampling distribution.
Just like the mean, one can obtain the variance for each sample and plot the frequency distribution, which appears skewed to the right.
Even in this case, if the sample size is large, the mean of the sample variances is close to the population variance.
If one considers the proportion of odd numbers in each sample and plots the graph, the distribution follows approximately a normal distribution pattern.
Similar to mean and variance, if the sample size is large, the mean of the sample proportions is close to the population proportion.
Gegeven enkelvoudige aselecte steekproeven van grootte n uit een gegeven populatie met een gemeten kenmerk, zoals het gemiddelde, de proportie of de standaarddeviatie voor elke steekproef, wordt de kansverdeling van al deze gemeten kenmerken de steekproefverdeling genoemd. De mate waarin een statistiek varieert van de ene steekproef tot de andere, wordt aangeduid als de steekproefvariabiliteit van een statistiek. De steekproefvariabiliteit van een statistiek wordt doorgaans gemeten aan de hand van de standaardfout. De standaardfout van het gemiddelde is een voorbeeld van een standaardfout. Dit is een specifieke standaarddeviatie en staat bekend als de standaarddeviatie van de steekproefverdeling van het gemiddelde.
Deze tekst is een bewerking van Openstax, Inleidende statistieken, sectie 2.7 Maatstaven voor de spreiding van gegevens
Consider spinning ten picker wheels and finding the mean of outcomes. This process is repeated, say 20,000 times.
The sample mean obtained for each repetition of the process is plotted, which looks similar to a normal distribution graph.
If the sample size is large, the distribution gets closer to the normal distribution, and the mean of the sample means gets closer to the population mean.
Such distribution of values of a statistic such as mean, variance, or a sample proportion is known as the sampling distribution.
Just like the mean, one can obtain the variance for each sample and plot the frequency distribution, which appears skewed to the right.
Even in this case, if the sample size is large, the mean of the sample variances is close to the population variance.
If one considers the proportion of odd numbers in each sample and plots the graph, the distribution follows approximately a normal distribution pattern.
Similar to mean and variance, if the sample size is large, the mean of the sample proportions is close to the population proportion.
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