Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
-When investigating times required for drive-through service, the following results (in seconds) were obtained. $ \begin{array}{lllllllll}\text { Restaurant A } & 120 & 67 & 89 & 97 & 124 & 68 & 72 & 96\end{array} $
$ \begin{array}{lllllllll}\text { Restaurant B } & 115 & 126 & 49 & 56 & 98 & 76 & 78 & 95\end{array} $

A) Restaurant A: $75 \mathrm { sec } ; 493.98 \mathrm { sec } ^ { 2 } ; 22.23 \mathrm { sec }$
Restaurant B: $70 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 26.98 \mathrm { sec }$
There is more variation in the times for restaurant $B$.
B) Restaurant A: $57 \mathrm { sec } ; 793.98 \mathrm { sec } ^ { 2 } ; 28.18 \mathrm { sec }$
Restaurant B: $77 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 26.98 \mathrm { sec }$
There is more variation in the times for restaurant A.
C) Restaurant A: $57 \mathrm { sec } ; 493.98 \mathrm { sec } ^ { 2 } ; 22.23 \mathrm { sec }$
Restaurant B: $77 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 26.98 \mathrm { sec }$
There is more variation in the times for restaurant $B$.
D) Restaurant A: $57 \mathrm { sec } ; 493.98 \mathrm { sec } ^ { 2 } ; 22.23 \mathrm { sec }$
Restaurant B: $56 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 32.89 \mathrm { sec }$
There is more variation in the times for restaurant $B$.

Question

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
-When investigating times required for drive-through service, the following results (in seconds) were obtained. $ \begin{array}{lllllllll}\text { Restaurant A } & 120 & 67 & 89 & 97 & 124 & 68 & 72 & 96\end{array} $
$ \begin{array}{lllllllll}\text { Restaurant B } & 115 & 126 & 49 & 56 & 98 & 76 & 78 & 95\end{array} $

A) Restaurant A: $75 \mathrm { sec } ; 493.98 \mathrm { sec } ^ { 2 } ; 22.23 \mathrm { sec }$
Restaurant B: $70 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 26.98 \mathrm { sec }$
There is more variation in the times for restaurant $B$.
B) Restaurant A: $57 \mathrm { sec } ; 793.98 \mathrm { sec } ^ { 2 } ; 28.18 \mathrm { sec }$
Restaurant B: $77 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 26.98 \mathrm { sec }$
There is more variation in the times for restaurant A.
C) Restaurant A: $57 \mathrm { sec } ; 493.98 \mathrm { sec } ^ { 2 } ; 22.23 \mathrm { sec }$
Restaurant B: $77 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 26.98 \mathrm { sec }$
There is more variation in the times for restaurant $B$.
D) Restaurant A: $57 \mathrm { sec } ; 493.98 \mathrm { sec } ^ { 2 } ; 22.23 \mathrm { sec }$
Restaurant B: $56 \mathrm { sec } ; 727.98 \mathrm { sec } ^ { 2 } ; 32.89 \mathrm { sec }$
There is more variation in the times for restaurant $B$.

Quizplus · Accepted Answer

The range for both samples is not given, but the variance and standard deviation are provided. By comparing the variance and standard deviation of both samples, we can see that they are lower for Restaurant A, indicating less variation in the drive-through times. Therefore, we can conclude that the best choice is C, where the range for Restaurant A is lower than that of Restaurant B, and the variance and standard deviation for Restaurant A are lower than those for Restaurant B.

Find the Range, Variance, and Standard Deviation for Each of the Two