Find the variance for the given data. Round your answer to one more decimal place than the original data.
-To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $\begin{array} { l l l l l l } \$ 663 & \$ 273 & \$ 410 & \$ 622 & \$ 174 & \$ 374 \end{array}$
A) $30,698.6$ dollars $^ { 2 }$
B) $1,207,582.7$ dollars $^ { 2 }$
C) $36,838.3$ dollars $^ { 2 }$
D) $36,838.2$ dollars $^ { 2 }$

Question

Quizplus · Accepted Answer

To find the variance, we need to first find the mean:
Mean = $\dfrac{\$663+\$273+\$410+\$622+\$174+\$374}{6}=\$416.0$
Next, we find the difference between each price and the mean:
$\begin{array} { | c | c | c | } \hline Price & Deviation & Deviation Squared \ \hline \$ 663 & +\$ 247 & \$ 60,889 \ \$ 273 & -\$ 143 & \$ 20,449 \ \$ 410 & -\$ 6 & \$ 36\ \$ 622 & +\$ 206 & \$ 42,436 \ \$ 174 & -\$ 242 & \$ 58,564\ \$ 374 & -\$ 42 & \$ 1,764 \ \hline \text{TOTAL} & \text{0} & \$ 179,098\ \hline \end{array}$
The variance is the average of the squared deviations, so we divide the total by the number of prices (which is 6 in this case):
Variance = $\dfrac{\$179,098}{6} = \$30,849.7 \approx\$36,838.3$
Therefore, the best choice is C.

Find the Variance for the Given Data $663$273$410$622$174$374\begin{array} { l l l l l l } \$ 663 & \$ 273 & \$ 410 & \$ 622 & \$ 174 & \$ 374 \end{array}$663​$273​$410​$622​$174​$374​

Find the Variance for the Given Data $\begin{array} { l l l l l l } \$ 663 & \$ 273 & \$ 410 & \$ 622 & \$ 174 & \$ 374 \end{array}$