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:

Stockholders' Equity

Stockholders' Equity represents the ownership interest of shareholders in the net assets of a company, calculated as the difference between total assets and total liabilities.

Revenues

Revenues represent the income earned by a business from its normal operations, such as sales of goods or services, before any expenses are deducted.

Assets

Resources owned or controlled by a business, expected to bring future economic benefits.

Expenses

Costs incurred in the process of earning revenue, including operational expenses like rent, utilities, and payroll.