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Sampling Error Formula

Statistical error arising out of nature of sampling, is known as sampling error. The error in statistical analysis arise because of unrepresentativeness of the observation in the samples taken.

For example, the weight of two thousand citizens from a country of two million is taken and the average weight is taken out from that, then it’s not the same as the average weight of the two million people in the country.

Since to determine the characteristics of a whole population the sampling is done, the difference between the sample values and population is called sampling error. We should note that the exact value of sampling cannot be done since the population value if not known  although often sampling error can be found out by probabilistic modelling of sample.

Thus the sampling error formula is given by

\[\large Sampling\;Error=\pm \sqrt{\frac{2500}{Sample\;Size}}\times 1.96\]

Solved Examples

Question: What is the sampling error if the average weight of 60 men is 58 kg?


Sampling error can be found out using the formula: $=\pm \sqrt{\frac{2500}{Sample\;Size}}\times 1.96$  

$=\pm \sqrt{\frac{2500}{60}}\times 1.96$

$=\pm 12.65$

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