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

question 176

Short Answer

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.

$\begin{array}{c|c|c|c|c|c|c|c|c}\text { Restaurant A } & 120 & 67 & 89 & 97 & 124 & 68 & 72 & 96 \\\hline \text { Restaurant B } & 115 & 126 & 49 & 56 & 98 & 76 & 78 & 95\end{array}$

A) 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 $B$ .

B) 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 $\mathrm { B }$ .

C) 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 $B$ .

D) 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 $\mathrm { A }$ .

• A) 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 \(B\).
• B) 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 \(\mathrm { B }\).
• C) 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 \(B\).
• D) 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 \(\mathrm { A }\).

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Definitions:

Reposition

The act or process of placing or arranging something in a different position.

Excursion

The movement of a structure or part away from its resting position, often used in the context of muscle movement or joint mobility.

Extension

The movement by which the two ends of any jointed part are drawn away from each other, increasing the angle between them.

Adduction

The movement of a limb or other body part toward the midline of the body or toward another body part.