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Find the sample standard deviation of the dataset
$x = 37$, $26$, $33$, $29$, $30$, $35$, $43$, $36$, $42$, $37$.
Find the sample mean. Hint: The sample mean is given by the formula $\bar{x} = \dfrac{\sum x}{n}$.
$\bar{x} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}} = \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{AR}}\hspace{54px}}~}$ $\bar{x} = \dfrac{[348]}{[10]} = [\dfrac{174}{5}]$
Complete the table.
$x$$x - \bar{x}$$(x - \bar{x})^2$
$37$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1}}\hspace{80px}}~}$
$26$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1}}\hspace{80px}}~}$
$33$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1}}\hspace{80px}}~}$
$29$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1}}\hspace{80px}}~}$
$30$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c1}}\hspace{80px}}~}$
$35$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c1}}\hspace{80px}}~}$
$43$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c1}}\hspace{80px}}~}$
$36$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c1}}\hspace{80px}}~}$
$42$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c1}}\hspace{80px}}~}$
$37$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c0}}\hspace{54px}}~}$$\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$$x - \bar{x}$$(x - \bar{x})^2$
$37$$[\dfrac{11}{5}]$$[\dfrac{121}{25}]$
$26$$[-\dfrac{44}{5}]$$[\dfrac{1936}{25}]$
$33$$[-\dfrac{9}{5}]$$[\dfrac{81}{25}]$
$29$$[-\dfrac{29}{5}]$$[\dfrac{841}{25}]$
$30$$[-\dfrac{24}{5}]$$[\dfrac{576}{25}]$
$35$$[\dfrac{1}{5}]$$[\dfrac{1}{25}]$
$43$$[\dfrac{41}{5}]$$[\dfrac{1681}{25}]$
$36$$[\dfrac{6}{5}]$$[\dfrac{36}{25}]$
$42$$[\dfrac{36}{5}]$$[\dfrac{1296}{25}]$
$37$$[\dfrac{11}{5}]$$[\dfrac{121}{25}]$
$[\dfrac{1338}{5}]$
Find the sample variance. Hint: The sample variance is given by the formula $s^2 = \dfrac{\sum (x - \bar{x})^2}{n-1}$.
$s^2 = \dfrac{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{80px}}~}}{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C2}}\hspace{80px}}~}} = \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{CR}}\hspace{100px}}~}$ $s^2 = \dfrac{[\dfrac{1338}{5}]}{[9]} = [\dfrac{446}{15}]$
Therefore, Hint: The standard deviation is the square root of the variance.
$s = \sqrt{\class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{D1}}\hspace{100px}}~}} = \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{DR}}\hspace{100px}}~}$ $s = \sqrt{[\dfrac{446}{15}]} = [5.45282801]$