Answer
The sample standard deviation of the data measured by the technician is $0.0001$ mm.
Work Step by Step
$7.0036\text{mm},$ $7.0035$mm, $7.0038$mm, $7.0035$mm, $7.0036$mm
The sum of the all measured values is,
$7.0036+7.0035+7.0038+7.0035+7.0036=35.018$
The number of the measured value is $5$.
Thus, the mean of the data is,
$\begin{align}
& \text{Mean}=\frac{\text{Sum of the all measured value}}{\text{Number of the measured value}} \\
& \text{Mean}=\frac{35.018}{5} \\
& \text{Mean}=7.0036 \\
\end{align}$
The difference of the data about the mean is,
$7.0036-7.0036=0$
And,
$7.0035-7.0036=-0.0001$
And,
$7.0038-7.0036=-0.0002$
And,
$7.0035-7.0036=-0.0001$
And,
$7.0036-7.0036=0$
Squaring the differenced data gives:
${{\left( 0 \right)}^{2}}=0$
And,
${{\left( -0.0001 \right)}^{2}}=0.00000001$
And,
${{\left( -0.0002 \right)}^{2}}=0.00000004$
And,
${{\left( -0.0001 \right)}^{2}}=0.00000001$
And,
${{\left( 0 \right)}^{2}}=0$
Sum of all squared data above is
$0+0.00000001+0.00000004+0.00000001+0=0.00000006$
Dividing the sum of the square data by the number of observations less one gives
$\frac{0.00000006}{5-1}=0.000000015$
Therefore, the sample standard deviation of the data is
$\sqrt{0.000000015}=0.0001$
Thus, the sample standard deviation of the data measured by the technician is $0.0001$ mm.
