Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. $5,2,5 , - 4,0,16$
A) $s = 46$
B) $s = 13.56$
C) $s = 20.34$
D) $s = 16$
E) $s = 6.78$

Question

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places.   $5,2,5 , - 4,0,16$  
A) $s = 46$
B) $s = 13.56$
C) $s = 20.34$
D) $s = 16$
E) $s = 6.78$

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 data points, and $\bar{x}$ is the mean of the data. For the given data $5, 2, 5, -4, 0, 16$, the mean $\bar{x} = \frac{5 + 2 + 5 - 4 + 0 + 16}{6} = \frac{24}{6} = 4$. The sum of squared deviations from the mean is $(5-4)^2 + (2-4)^2 + (5-4)^2 + (-4-4)^2 + (0-4)^2 + (16-4)^2 = 1 + 4 + 1 + 64 + 16 + 144 = 230$. Thus, $s = \sqrt{\frac{230}{6-1}} = \sqrt{\frac{230}{5}} = \sqrt{46} \approx 6.78$.

Compute the (Sample) Standard Deviation for the Data 5,2,5,−4,0,165,2,5 , - 4,0,165,2,5,−4,0,16

Compute the (Sample) Standard Deviation for the Data $5,2,5 , - 4,0,16$