Question

The following numbers are tire pressures in pai (pounds per square inch) 320 31.3 217 243 39.1 31.1 27.4 Compute the sample mean·sample variance, sample standard deviation, and sample tange. Include a ,小. unit with each answer.

Answer 1

${\color{Blue} \mathbf{Solution}}$

$sample\;mean\;(\bar x)=\frac{\sum x_i}{n}=\frac{206.9}{7}=\mathbf{{\color{Red} 29.56}}\;pounds\; per \;square\; inch$

$sample\;variance\;(s^{2})=\frac{\sum x_i^{2}-\frac{\left ( \sum x_i \right )^{2}}{n}}{n-1}$

$sample\;variance\;(s^{2})=\frac{6311.85-\frac{\left ( 206.9 \right )^{2}}{7}}{7-1}$

$sample\;variance\;(s^{2})={\color{Red} \mathbf{32.75}}\;pounds\; per \;square\; inch$

$sample\;standard\;deviation\;(s)=\sqrt{variance} =\sqrt{32.75}={\color{Red} \mathbf{5.72}}\;pounds\; per \;square\; inch$

$sample\;range=max-min=39.1-21.7={\color{Red} \mathbf{17.4}}\;pounds\; per \;square\; inch$