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A population consists of the following N = 6 scores:2, 4, 1, 2, 7, 2.Compute µ and σ for the population.

Sagot :

Given:

Scores 2, 4, 1, 2, 7, 2

N = 6

The population mean is computed by using the following formula:

[tex]\mu=\frac{2+4+1+2+7+2}{6}=\frac{18}{6}=3[/tex]

Therefore, the population mean is 3

The standard deviation is given by:

[tex]\sigma=\sqrt{\frac{(2-3)^2+(4-3)^2+(1-3)^2+(2-3)^2+(7-3)^2+(2-3)^2}{6}}[/tex]

Simplify:

[tex]\begin{gathered} \sigma=\sqrt{\frac{(-1)^2+(1)^2+(-2)^2+(-1)^2+(4)^2+(-1)^2}{6}} \\ \sigma=\sqrt{\frac{1+1+4+1+16+1}{6}} \\ \sigma=\sqrt{\frac{24}{6}}=\sqrt{4}=2 \end{gathered}[/tex]

Answer:

[tex]\begin{gathered} \mu=3 \\ \sigma=2 \end{gathered}[/tex]

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