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

question 175

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.

$\begin{array}{l|l|l|l|l|l|l|l|l}\text { Restaurant A } & 120 & 123 & 153 & 128 & 124 & 118 & 154 & 110 \\\hline \text { Restaurant B } & 115 & 126 & 147 & 156 & 118 & 110 & 145 & 137\end{array}$

A) Restaurant A: $44 \mathrm { sec } ; 260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }$
Restaurant B: $46 \mathrm { sec } ; 245.64 \mathrm { sec } ^ { 2 } ; 15.67 \mathrm { sec }$
There is more variation in the times for restaurant A.

B) Restaurant A: 46 sec; $260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }$
Restaurant B: $44 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }$
There is more variation in the times for restaurant $\mathrm { B }$ .

C) Restaurant A: $44 \mathrm { sec } ; 298.34 \mathrm { sec } ^ { 2 } ; 17.27 \mathrm { sec }$
Restaurant B: $46 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }$
There is more variation in the times for restaurant A.

D) Restaurant A: $44 \mathrm { sec } ; 260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }$
Restaurant B: $46 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }$
There is more variation in the times for restaurant $B$ .

• A) Restaurant A: \(44 \mathrm { sec } ; 260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }\)
• Restaurant B: \(46 \mathrm { sec } ; 245.64 \mathrm { sec } ^ { 2 } ; 15.67 \mathrm { sec }\)
• There is more variation in the times for restaurant A.
• B) Restaurant A: 46 sec; \(260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }\)
• Restaurant B: \(44 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }\)
• There is more variation in the times for restaurant \(\mathrm { B }\).
• C) Restaurant A: \(44 \mathrm { sec } ; 298.34 \mathrm { sec } ^ { 2 } ; 17.27 \mathrm { sec }\)
• Restaurant B: \(46 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }\)
• There is more variation in the times for restaurant A.
• D) Restaurant A: \(44 \mathrm { sec } ; 260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }\)
• Restaurant B: \(46 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }\)
• There is more variation in the times for restaurant \(B\).

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Definitions:

Min Function

A mathematical function used to determine the smallest value among a set of numbers or inputs.

Income

A measure of money received on a regular basis, either through employment, business, investments, or other sources.

Price of X

The specific cost or value associated with a particular item or commodity, denoted as "X."

Price of Y

The monetary cost or value assigned to a good or service, labeled as 'Y'.