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Find the sample standard deviation of the dataset
$x = 210.6$, $206.1$, $206$, $217.3$, $225.2$, $219.5$, $207.8$, $213.1$, $226.6$, $211.8$, $205.6$, $205.8$, $218.3$.
Find the sample mean. Hint: The sample mean is given by the formula $\bar{x} = \dfrac{\sum x}{n}$.
$\bar{x} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}} = \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{AR}}\hspace{54px}}~}$ $\bar{x} = \dfrac{2773.7}{13} = 213.36153846$
Complete the table.
$x$$x - \bar{x}$$(x - \bar{x})^2$
$210.6$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1}}\hspace{80px}}~}$
$206.1$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1}}\hspace{80px}}~}$
$206$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1}}\hspace{80px}}~}$
$217.3$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1}}\hspace{80px}}~}$
$225.2$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c1}}\hspace{80px}}~}$
$219.5$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c1}}\hspace{80px}}~}$
$207.8$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c1}}\hspace{80px}}~}$
$213.1$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c1}}\hspace{80px}}~}$
$226.6$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c1}}\hspace{80px}}~}$
$211.8$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c1}}\hspace{80px}}~}$
$205.6$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c1}}\hspace{80px}}~}$
$205.8$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c0}}\hspace{54px}}~}$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c1}}\hspace{80px}}~}$
$218.3$$\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c0}}\hspace{54px}}~}$$\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$
$210.6$$-2.76153846$$7.62609467$
$206.1$$-7.26153846$$52.72994083$
$206$$-7.36153846$$54.19224852$
$217.3$$3.93846154$$15.51147929$
$225.2$$11.83846154$$140.1491716$
$219.5$$6.13846154$$37.68071006$
$207.8$$-5.56153846$$30.93071006$
$213.1$$-0.26153846$$0.06840237$
$226.6$$13.23846154$$175.25686391$
$211.8$$-1.56153846$$2.43840237$
$205.6$$-7.76153846$$60.24147929$
$205.8$$-7.56153846$$57.17686391$
$218.3$$4.93846154$$24.38840237$
$658.39076923$
Find the sample variance. Hint: The sample variance is given by the formula $s^2 = \dfrac{\sum (x - \bar{x})^2}{n-1}$.
$s^2 = \dfrac{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{80px}}~}}{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C2}}\hspace{80px}}~}} = \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{CR}}\hspace{100px}}~}$ $s^2 = \dfrac{658.39076923}{12} = 54.86589744$
Therefore, Hint: The standard deviation is the square root of the variance.
$s = \sqrt{\class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{D1}}\hspace{100px}}~}} = \class{inputBox step4}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{DR}}\hspace{100px}}~}$ $s = \sqrt{54.86589744} = 7.40715178$