Question

Find the range and standard deviation of the set of data 5, 9, 10, 12, 14, 16 The range is 11 (Simplify your answer) The standard deviation is (Round the final answer to the nearest hundredth as needed Round all intermediate values to the nearest hundredth as needed

Answer 1

$\small \begin{tabular}{rrr} \hline X & X - mean & (X-mean)\^{}2 \\ \hline 5 & -6 & 36 \\ 9 & -2 & 4 \\ 10 & -1 & 1 \\ 12 & 1 & 1 \\ 14 & 3 & 9 \\ 16 & 5 & 25 \\ \hline \end{tabular}$
a) Since we know that
The range is the difference between the largest and smallest values in a set of values.
This implies that
Range = 16.0-5.0
Range = 11.0
b) Since we know that
$\small \\Variance(s^2) = \frac{(\sum{x_i - \bar{x}})^2}{n-1} \\(\sum{x_i - \bar{x}})^2 = 76.0 \\n = 6 \\Variance(s^2) = \frac{76.0}{5} \\Variance(s^2) = 15.2 \\Standard\;Deviation(s) = \sqrt{Variance} \\Standard\;Deviation(s) = 3.90$
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