Answered

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

\begin{tabular}{|l|l|l|}
\hline \multicolumn{3}{|l|}{ Coffee Ground } \\
\hline 1.5 & 20 & 3.5 \\
\hline 12 & 2 & 4 \\
\hline 11 & 7 & 2.5 \\
\hline 9.5 & 3 & 5 \\
\hline
\end{tabular}

\begin{tabular}{|l|l|l|}
\hline \multicolumn{3}{|l|}{ Perks [tex]$A$[/tex] Lot } \\
\hline 10 & 3.5 & 3 \\
\hline 5 & 2.5 & 7 \\
\hline 8 & 5.5 & 9.5 \\
\hline 6 & 9 & 4.5 \\
\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. Perks A Lot, with a mean value of 6.125 gallons
B. Perks A Lot, with a median value of 6.125 gallons
C. Coffee Ground, with a mean value of 6.75 gallons
D. Coffee Ground, with a median value of 6.75 gallons



Answer :

GinnyAnswer
To determine which shop typically sells the most amount of coffee per hour, we need to examine both the mean and median values of the gallons of coffee sold per hour for both shops. Here is a step-by-step analysis:

### Coffee Ground

1. Data: The given data for Coffee Ground is:
[tex]\[ 1.5, 20, 3.5, 12, 2, 4, 11, 7, 2.5, 9.5, 3, 5 \][/tex]

2. Mean: The mean is the average value of the dataset.
- Calculated Mean: 6.75

3. Median: The median is the middle value when the data is ordered from least to greatest.
- Ordered Data: 1.5, 2, 2.5, 3, 3.5, 4, 5, 7, 9.5, 11, 12, 20
- Position of Median: The median for a dataset of 12 values is the average of the 6th and 7th values.
- Calculated Median: 4.5

### Perks A Lot

1. Data: The given data for Perks A Lot is:
[tex]\[ 10, 3.5, 3, 5, 2.5, 7, 8, 5.5, 9.5, 6, 9, 4.5 \][/tex]

2. Mean: The mean is the average value of the dataset.
- Calculated Mean: 6.125

3. Median: The median is the middle value when the data is ordered from least to greatest.
- Ordered Data: 2.5, 3, 3.5, 4.5, 5, 5.5, 6, 7, 8, 9, 9.5, 10
- Position of Median: The median for a dataset of 12 values is the average of the 6th and 7th values.
- Calculated Median: 5.75

### Comparison

- Mean Values:
- Coffee Ground: 6.75
- Perks A Lot: 6.125

- Median Values:
- Coffee Ground: 4.5
- Perks A Lot: 5.75

### Conclusion

- When comparing the mean values, Coffee Ground has a higher mean (6.75 gallons) compared to Perks A Lot (6.125 gallons). This indicates that, on average, Coffee Ground sells slightly more coffee per hour than Perks A Lot.
- When comparing the median values, Perks A Lot has a higher median (5.75 gallons) compared to Coffee Ground (4.5 gallons). This suggests that the typical amount of coffee sold per hour is more for Perks A Lot when considering the median, which can be considered a measure less affected by extreme values (like the maximum of 20 at Coffee Ground).

Given that the mean value is often a better measure of central tendency in the absence of extreme outliers and given the detailed data, Coffee Ground with a mean value of 6.75 gallons typically sells the most amount of coffee per hour.