cheniyahmartin05
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The data given represents the number of gallons of coffee sold per hour at two different coffee shops.

\begin{tabular}{|l|l|l|l|l|l|}
\hline \multicolumn{3}{|c|}{ Coffee Ground } & \multicolumn{3}{|c|}{ Wide Awake } \\
\hline 1.5 & 20 & 3.5 & 2.5 & 10 & 4 \\
\hline 12 & 2 & 5 & 18 & 4 & 3 \\
\hline 11 & 7 & 2.5 & 3 & 6.5 & 15 \\
\hline 9.5 & 3 & 5 & 6 & 5 & 2.5 \\
\hline
\end{tabular}

Compare the data and use the correct measure of center to determine which shop typically sells the most coffee per hour. Explain.

A. Wide Awake, with a median value of 4.5 gallons
B. Wide Awake, with a mean value of about 4.5 gallons
C. Coffee Ground, with a mean value of about 5 gallons
D. Coffee Ground, with a median value of 5 gallons



Answer :

GinnyAnswer
To address this problem, we first need to determine the appropriate measures of center for both coffee shops. For each coffee shop, we will calculate the mean (average) and the median gallons of coffee sold per hour. These measures will help us compare the typical sales between the two shops.

Coffee Ground:
- Data: 1.5, 20, 3.5, 12, 2, 5, 11, 7, 2.5, 9.5, 3, 5

Wide Awake:
- Data: 2.5, 10, 4, 18, 4, 3, 3, 6.5, 15, 6, 5, 2.5

### Calculation of Mean:

1. Coffee Ground Mean:
- Sum of Coffee Ground data: [tex]\(1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5 + 9.5 + 3 + 5 = 82\)[/tex]
- Number of data points: 12
- Mean (Average) = Total Sum / Number of Data Points
- Mean for Coffee Ground: [tex]\( \frac{82}{12} \approx 6.833\)[/tex]

2. Wide Awake Mean:
- Sum of Wide Awake data: [tex]\(2.5 + 10 + 4 + 18 + 4 + 3 + 3 + 6.5 + 15 + 6 + 5 + 2.5 = 79.5\)[/tex]
- Number of data points: 12
- Mean for Wide Awake: [tex]\( \frac{79.5}{12} \approx 6.625\)[/tex]

### Calculation of Median:

1. Coffee Ground Median:
- Sorted data: 1.5, 2, 2.5, 3, 3.5, 5, 5, 7, 9.5, 11, 12, 20
- Number of data points: 12
- Median (Middle Value) is the average of the 6th and 7th values because the data count is even.
- Median for Coffee Ground: [tex]\( \frac{5 + 5}{2} = 5\)[/tex]

2. Wide Awake Median:
- Sorted data: 2.5, 2.5, 3, 3, 4, 4, 5, 6, 6.5, 10, 15, 18
- Number of data points: 12
- Median is the average of the 6th and 7th values.
- Median for Wide Awake: [tex]\( \frac{4 + 5}{2} = 4.5\)[/tex]

### Comparison and Conclusion:
- Mean for Coffee Ground: 6.833
- Mean for Wide Awake: 6.625
- Median for Coffee Ground: 5.0
- Median for Wide Awake: 4.5

By comparing these values, we observe that:
- The mean value is higher for Coffee Ground (6.833 vs. 6.625 for Wide Awake).
- The median value is also higher for Coffee Ground (5.0 vs. 4.5 for Wide Awake).

Thus, Coffee Ground typically sells more coffee per hour based on both the mean and median values:

- Coffee Ground, with a mean value of about 6.83 gallons
- Coffee Ground, with a median value of 5 gallons

Given the options presented in the question, the correct choice is:
Coffee Ground, with a median value of 5 gallons.

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