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Find the population standard deviation of the dataset
$x = 78$, $72$, $66$, $67$, $71$, $77$, $83$, $79$, $74$, $82$.
Find the population mean. Hint: The population mean is given by the formula $\mu = \dfrac{\sum x}{n}$.
$\mu = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}} = \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{AR}}\hspace{54px}}~}$ $\mu = \dfrac{[749]}{[10]} = [\dfrac{749}{10}]$
Complete the table.
$x$$x - \mu$$(x - \mu)^2$
$78$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1}}\hspace{80px}}~}$
$72$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1}}\hspace{80px}}~}$
$66$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1}}\hspace{80px}}~}$
$67$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1}}\hspace{80px}}~}$
$71$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c1}}\hspace{80px}}~}$
$77$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c1}}\hspace{80px}}~}$
$83$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c1}}\hspace{80px}}~}$
$79$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c1}}\hspace{80px}}~}$
$74$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c1}}\hspace{80px}}~}$
$82$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c1}}\hspace{80px}}~}$
$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{BR}}\hspace{80px}}~}$
$x$$x - \mu$$(x - \mu)^2$
$78$$[\dfrac{31}{10}]$$[\dfrac{961}{100}]$
$72$$[-\dfrac{29}{10}]$$[\dfrac{841}{100}]$
$66$$[-\dfrac{89}{10}]$$[\dfrac{7921}{100}]$
$67$$[-\dfrac{79}{10}]$$[\dfrac{6241}{100}]$
$71$$[-\dfrac{39}{10}]$$[\dfrac{1521}{100}]$
$77$$[\dfrac{21}{10}]$$[\dfrac{441}{100}]$
$83$$[\dfrac{81}{10}]$$[\dfrac{6561}{100}]$
$79$$[\dfrac{41}{10}]$$[\dfrac{1681}{100}]$
$74$$[-\dfrac{9}{10}]$$[\dfrac{81}{100}]$
$82$$[\dfrac{71}{10}]$$[\dfrac{5041}{100}]$
$[\dfrac{3129}{10}]$
Find the population variance. Hint: The population variance is given by the formula $\sigma^2 = \dfrac{\sum (x - \mu)^2}{n}$.
$\sigma^2 = \dfrac{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{80px}}~}}{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C2}}\hspace{80px}}~}} = \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{CR}}\hspace{100px}}~}$ $\sigma^2 = \dfrac{[\dfrac{3129}{10}]}{[10]} = [\dfrac{3129}{100}]$
Therefore, Hint: The standard deviation is the square root of the variance.
$\sigma = \sqrt{\class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{D1}}\hspace{100px}}~}} = \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{DR}}\hspace{100px}}~}$ $\sigma = \sqrt{[\dfrac{3129}{100}]} = [5.59374651]$