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Find the sample standard deviation of the dataset
$x = 477.17$, $488.4$, $486.76$, $480.05$, $490.34$, $495.26$, $477.48$, $473.45$, $488.75$, $482.74$, $496.97$, $480.87$, $472.07$.
Find the sample mean. Hint: The sample mean is given by the formula $\bar{x} = \dfrac{\sum x}{n}$.
$\bar{x} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}} = \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{AR}}\hspace{54px}}~}$ $\bar{x} = \dfrac{[6290.31]}{[13]} = [483.87]$
Complete the table.
$x$$x - \bar{x}$$(x - \bar{x})^2$
$477.17$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1}}\hspace{80px}}~}$
$488.4$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1}}\hspace{80px}}~}$
$486.76$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1}}\hspace{80px}}~}$
$480.05$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1}}\hspace{80px}}~}$
$490.34$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c1}}\hspace{80px}}~}$
$495.26$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c1}}\hspace{80px}}~}$
$477.48$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c1}}\hspace{80px}}~}$
$473.45$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c1}}\hspace{80px}}~}$
$488.75$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c1}}\hspace{80px}}~}$
$482.74$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c1}}\hspace{80px}}~}$
$496.97$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c1}}\hspace{80px}}~}$
$480.87$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c1}}\hspace{80px}}~}$
$472.07$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c1}}\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$
$477.17$$[-6.7]$$[44.89]$
$488.4$$[4.53]$$[20.5209]$
$486.76$$[2.89]$$[8.3521]$
$480.05$$[-3.82]$$[14.5924]$
$490.34$$[6.47]$$[41.8609]$
$495.26$$[11.39]$$[129.7321]$
$477.48$$[-6.39]$$[40.8321]$
$473.45$$[-10.42]$$[108.5764]$
$488.75$$[4.88]$$[23.8144]$
$482.74$$[-1.13]$$[1.2769]$
$496.97$$[13.1]$$[171.61]$
$480.87$$[-3.]$$[9.]$
$472.07$$[-11.8]$$[139.24]$
$[754.2982]$
Find the sample variance. Hint: The sample variance is given by the formula $s^2 = \dfrac{\sum (x - \bar{x})^2}{n-1}$.
$s^2 = \dfrac{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{80px}}~}}{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C2}}\hspace{80px}}~}} = \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{CR}}\hspace{100px}}~}$ $s^2 = \dfrac{[754.2982]}{[12]} = [62.85818333]$
Therefore, Hint: The standard deviation is the square root of the variance.
$s = \sqrt{\class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{D1}}\hspace{100px}}~}} = \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{DR}}\hspace{100px}}~}$ $s = \sqrt{[62.85818333]} = [7.92831529]$