Central Limit Theorem and Standard Error

Central Limit Theorem and Standard Error – Example 1:

Central Limit Theorem and Standard Error – Example 2:

Solution: First, find the mean of the given data.

Mean\(=\frac{4+8+12+16+20}{5}=12\)

Now, the standard deviation can be calculated as;

\(S=\frac{Summation\:of\:difference\:between\:each\:value\:of\:given\:data\:and\:the\:mean\:value}{Number\:of\:values}\)

\(S=\sqrt{\frac{\left(4-12\right)^2+\left(8-12\right)^2+\left(12-12\right)^2+\left(16-12\right)^2+\left(20-12\right)^2}{5}}\)

\(=5.65\)

So, use the \(SE\) formula: \(SE=\frac{σ}{\sqrt{n}}\)

\(SE=\frac{5.65}{\sqrt{5}}= 2.52\)

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