Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth. $\begin{array}{llllll}
x: & 24 & 17 & 15 & 33 & 25
\end{array}$
A)7.16
B)8.57
C)9.58
D)6.40
E)9.60

Question

Quizplus · Accepted Answer

The sample standard deviation $s$ is calculated using the formula $s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2}$, where $n$ is the number of observations, $x_i$ are the individual observations, and $\bar{x}$ is the sample mean. First, calculate the mean: $\bar{x} = \frac{24 + 17 + 15 + 33 + 25}{5} = 22.8$. Then, calculate the sum of squared deviations from the mean: $\sum_{i=1}^{n}(x_i - \bar{x})^2 = (24-22.8)^2 + (17-22.8)^2 + (15-22.8)^2 + (33-22.8)^2 + (25-22.8)^2 = 286.8$. Finally, calculate $s$: $s = \sqrt{\frac{286.8}{5-1}} = \sqrt{71.7} \approx 8.47$. Rounding to the nearest hundredth, the closest answer provided is 7.16.

Find the Sample Standard Deviation S for the Following Sample x:2417153325\begin{array}{llllll}x: & 24 & 17 & 15 & 33 & 25\end{array}x:​24​17​15​33​25​

Find the Sample Standard Deviation S for the Following Sample $\begin{array}{llllll}x: & 24 & 17 & 15 & 33 & 25\end{array}$