Find the sample standard deviation for the following data set: $\begin{array} { l l l l l }
22 & 13 & 34 & 27 & 18
\end{array}$
A) 7.2
B) 52.6
C) 65.7
D) 8.1

Question

Find the sample standard deviation for the following data set: $\begin{array} { l l l l l } 
22 & 13 & 34 & 27 & 18
\end{array}$
A) 7.2
B) 52.6
C) 65.7
D) 8.1

Quizplus · Accepted Answer

Using the formula for sample standard deviation:
$$s = \sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}$$
where $\bar{x}$ is the sample mean, $n$ is the sample size, and $x_i$ are the individual data points.

We first need to find the sample mean:
$$\bar{x} = \frac{22 + 13 + 34 + 27 + 18}{5} = 22.8$$

Next, we calculate the sum of squared differences from the mean:
$$\sum_{i=1}^{n}(x_i-\bar{x})^2 = (22-22.8)^2 + (13-22.8)^2 + (34-22.8)^2 + (27-22.8)^2 + (18-22.8)^2 = 560.8$$

Finally, we put everything together:
$$s = \sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}} = \sqrt{\frac{560.8}{4}} \approx \boxed{	ext{(D) 8.1}}$$

Find the Sample Standard Deviation for the Following Data Set 2213342718\begin{array} { l l l l l } 22 & 13 & 34 & 27 & 18\end{array}22​13​34​27​18​

Find the Sample Standard Deviation for the Following Data Set $\begin{array} { l l l l l } 22 & 13 & 34 & 27 & 18\end{array}$