Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l }
22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3
\end{array}$
A) 8.35
B) 3999.0
C) 4347.7
D) 36.1

Question

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l } 
22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3
\end{array}$
A) 8.35
B) 3999.0
C) 4347.7
D) 36.1

Quizplus · Accepted Answer

The standard deviation for a sample is calculated using the formula: $\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$, where $x_i$ are the data points, $\bar{x}$ is the mean of the data, and $n$ is the number of data points. First, calculate the mean: $\bar{x} = \frac{22.6 + 16.1 + 36.1 + 36.0 + 23.8 + 20.3}{6} = 25.82$. Then, calculate the sum of squared differences from the mean, divide by $n-1 = 5$, and take the square root. Doing this calculation gives a standard deviation of approximately 8.35, rounded to two decimal places as the original data is to one decimal place.

Find the Standard Deviation for the Given Sample Data 22.616.136.136.023.820.3\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}22.6​16.1​36.1​36.0​23.8​20.3​

Find the Standard Deviation for the Given Sample Data $\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}$