Estimators
From the unknown parameter to its point estimate: parameter and statistic, estimating a mean, a proportion and a variance (dividing by n − 1), bias, variance, convergence and mean squared error.
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A few cards from the deck
Sample: what is it?
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A part of a population, drawn at random, on which we measure what we would like to know about the whole population.
The whole population can almost never be measured: we measure the sample and deduce an approximate value, always affected by chance.
What does this program print?
```python
import statistics
t = [4, 6, 8]
print(statistics.variance(t), statistics.pvariance(t))`4 2.66666666666666652.6666666666666665 44 42.6666666666666665 2.6666666666666665
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4 2.6666666666666665variancetreats the list as a sample and divides by n − 1: 8 / 2 = 4.pvariancetreats it as a whole population and divides by n: 8 / 3.A … describes the population and stays fixed; a … is computed on the sample and changes from one draw to the next.
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A parameter describes the population and stays fixed; a statistic is computed on the sample and changes from one draw to the next.
The mean µ of every request of the year is a parameter; the mean of 40 requests drawn at random is a statistic used to estimate it.
Estimator: what is it?
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A formula applied to the data of a sample to approximate an unknown parameter of the population.
Since the sample is random, so is its value: two samples give two different values. The value obtained on a given sample is called the estimate.