Find the sample standard deviation from the set of measurements below. Please round your answer to the nearest ten thousandth. $0.2613 \text { in., } 0.2615 \text { in., } 0.2622 \text { in., } 0.2680 \text { in., } 0.2612 \text { in., } 0.2611 \text { in. }$
A) $S = 0.0025 \text { in. }$
B) $S = 0.0027 \text { in. }$
C) $S = 0.0021 \text { in. }$
D) $S = 0.0028 \text { in. }$
E) $S = 0.0026 \mathrm { in } .$

Question

Quizplus · Accepted Answer

The sample standard deviation is 0.0025 in. This can be calculated using the formula:$$s = \sqrt{\frac{\sum(x - \overline{x})^2}{n-1}}$$where x is each measurement, $\overline{x}$ is the mean of the measurements, and n is the number of measurements.In this case, the mean of the measurements is 0.2615 in. Plugging this into the formula, we get:$$s = \sqrt{\frac{(0.2613 - 0.2615)^2 + (0.2615 - 0.2615)^2 + (0.2622 - 0.2615)^2 + (0.2680 - 0.2615)^2 + (0.2612 - 0.2615)^2 + (0.2611 - 0.2615)^2}{6-1}}$$$$s = \sqrt{\frac{0.000004 + 0.000000 + 0.000005 + 0.000042 + 0.000001 + 0.000002}{5}}$$$$s = \sqrt{\frac{0.000054}{5}}$$$$s = 0.0025$$