Find the variance for the given data. Round your answer to one more decimal place than the original data.
-$$\begin{array} { l l l l l }
11.0 & 17.6 & 12.6 & 11.7 & 16.5
\end{array}$$
A) 7.08
B) 8.75
C) 48.98
D) 8.85

Question

Find the variance for the given data. Round your answer to one more decimal place than the original data.
-$$\begin{array} { l l l l l } 
11.0 & 17.6 & 12.6 & 11.7 & 16.5
\end{array}$$
A) 7.08
B) 8.75
C) 48.98
D) 8.85

Quizplus · Accepted Answer

First, we need to find the mean of the data:
\begin{align*}
	ext{Mean} &= \frac{11.0 + 17.6 + 12.6 + 11.7 + 16.5}{5}\
&= 13.48
\end{align*}
Next, we need to find the variance using the formula:
\begin{align*}
	ext{Variance} &= \frac{(x_1 - \bar{x})^2 + (x_2 - \bar{x})^2 + \cdots + (x_n - \bar{x})^2}{n-1}\
&= \frac{(11.0 - 13.48)^2 + (17.6 - 13.48)^2 + \cdots + (16.5 - 13.48)^2}{4}\
&= \frac{4.78 + 18.09 + 0.54 + 5.50 + 9.20}{4}\
&= 7.7775
\end{align*}
Finally, we round to one more decimal place than the original data, which gives:
\begin{align*}
	ext{Variance} &= 7.8
\end{align*}
Therefore, the best choice is D because it is the closest to 7.8.

Find the Variance for the Given Data 11.017.612.611.716.5\begin{array} { l l l l l } 11.0 & 17.6 & 12.6 & 11.7 & 16.5\end{array}11.0​17.6​12.6​11.7​16.5​

Find the Variance for the Given Data $\begin{array} { l l l l l } 11.0 & 17.6 & 12.6 & 11.7 & 16.5\end{array}$