Sampling Errors

The purpose of a sample is to produce one or more estimates of the population parameters (a parameter being the actual value of a characteristic of the whole population, such as its average income). A sampling error is the difference between the sample estimate and the corresponding population parameter — that is, between the true value and the value calculated from the sample.

Worked example. Take the incomes of 5 farmers of Manipur: 500, 550, 600, 650, 700. The true population mean is

$\dfrac{500+550+600+650+700}{5}=\dfrac{3000}{5}=600.$

Now suppose a sample of just two farmers is drawn, with incomes 500 and 600. The sample mean is

$\dfrac{500+600}{2}=\dfrac{1100}{2}=550.$

The sampling error is the true value minus the estimate: …