The standard deviation of the sampling distribution of a statistic is defined as the standard error of the statistic, which is abbreviated as SE.

**STANDARD ERROR**

The standard deviation of the sampling distribution of a statistic
is defined as the **standard** **error **of the statistic, which is abbreviated as** ***SE.*

For example, the standard deviation of the sampling distribution
of the sample mean, *x*, is known as the standard error of the sample
mean, or *SE* ().

If the random variables *X*_{1}, *X*_{2},
..., *X _{–n}* are independent and have the same distribution with
mean

Calculate the standard error of for the
sampling distribution obtained in *Example 1.*

Here, the population is {4, 8, 12, 16}.

Population size (*N*) = 4, Sample size (*n*) = 2

Population mean (*µ*) = (4 + 8 + 12+ 16)/4 = 40/4 = 10

The population variance is calculated as

This can also be verified from the sampling distribution of (see Table 1.3)

Hence, the standard deviation of the sampling distribution of is = √10 .

Standard Errors of some of the frequently referred statistics are
listed in Table 1.4.

Table 1.4 Statistics and their Standard Errors

Tags : Definition, Example Solved Problems | Statistics , 12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests

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12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests : Standard Error | Definition, Example Solved Problems | Statistics

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