Thank you for visiting A local cafΓ© serves tea coffee cookies scones and muffins They recently gathered data about their customers who purchase both a drink and a snack. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We begin by noting that the survey was of 500 customers, each purchasing one drink and one snack. The cafΓ© offers two drinks (tea and coffee) and three snacks (cookies, muffins, and scones). The incomplete frequency table is as follows:
[tex]$$
\begin{array}{|c|c|c|c|c|}
\hline
& \,\,\,\,?\,\,\, & \,\,\,\,?\,\,\, & \,\,\,\,?\,\,\, & \text{Total} \\
\hline
\text{Row 1: } & 40 & 100 & 110 & 250 \\
\hline
\text{Row 2: } & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
We are given two pieces of information:
1. Approximately [tex]$36\%$[/tex] of the customers (of 500) buy a muffin.
2. Approximately [tex]$24\%$[/tex] of the tea drinkers have a scone with their tea.
Letβs use these facts step by step.
βββββββββββββββββββββββββββββββββββββββ
Step 1. Identify the Muffin Column
The total number of customers who buy a muffin is
[tex]$$0.36 \times 500 = 180.$$[/tex]
Looking at the column totals, the column that sums to 180 must correspond to muffins. Hence, the column with total 180 is for muffins.
βββββββββββββββββββββββββββββββββββββββ
Step 2. Assign Drinks (Rows)
The only two drinks are tea and coffee. The table shows two rows with equal totals of 250 customers each. One row corresponds to tea drinkers and the other to coffee drinkers. We will decide which row is tea by using the second piece of information.
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Step 3. Match the Tea-Scone Information
We are told that approximately [tex]$24\%$[/tex] of the tea customers have a scone. Since there are 250 tea customers, we would ideally have
[tex]$$0.24 \times 250 = 60$$[/tex]
tea customers ordering scones. Inspect the two rows in the column βsconesβ (the column that is not yet assigned). The two values available in the unassigned scone column are [tex]$110$[/tex] and [tex]$50$[/tex]. No cell exactly gives 60, but the count [tex]$50$[/tex] is closer to the desired value (and within the range of approximation given the circumstances).
Thus, we assign the row containing [tex]$50$[/tex] in the scone column as the tea row. Consequently, the other row (with [tex]$110$[/tex] in the scone column) is the coffee row.
βββββββββββββββββββββββββββββββββββββββ
Step 4. Assign the Remaining Snack Columns
We already have:
- The column with total [tex]$180$[/tex] is muffins.
Now, the remaining two snack columns (with totals [tex]$160$[/tex] each) must be assigned among cookies and scones. Since we already determined from Step 3 that in the tea row the scone count is [tex]$50$[/tex], we choose the column that provides this [tex]$50$[/tex] for tea as the scone column. That leaves the other column (with total [tex]$160$[/tex]) to be cookies.
βββββββββββββββββββββββββββββββββββββββ
Step 5. Write the Final Table with Headings
The final assigned headings are:
- Drinks (rows):
- Row 1: Coffee
- Row 2: Tea
- Snacks (columns):
- Column 1: Cookies (total = 160)
- Column 2: Muffins (total = 180)
- Column 3: Scones (total = 160)
Thus, the completed table is:
[tex]$$
\begin{array}{|l|c|c|c|c|}
\hline
& \textbf{Cookies} & \textbf{Muffins} & \textbf{Scones} & \textbf{Total} \\
\hline
\textbf{Coffee} & 40 & 100 & 110 & 250 \\
\hline
\textbf{Tea} & 120 & 80 & 50 & 250 \\
\hline
\textbf{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
βββββββββββββββββββββββββββββββββββββββ
Step 6. Check the Conditions
1. Muffins: The muffin column total is [tex]$180$[/tex], which is exactly [tex]$36\%$[/tex] of 500 since [tex]$$\frac{180}{500} \times 100 = 36\%.$$[/tex]
2. Tea with scones: In the tea row, the scone count is [tex]$50$[/tex]. This is approximately [tex]$$\frac{50}{250} \times 100 = 20\%.$$[/tex]
Although [tex]$20\%$[/tex] is not exactly [tex]$24\%$[/tex], [tex]$50$[/tex] is the closest available value from the survey that can be assigned.
βββββββββββββββββββββββββββββββββββββββ
Conclusion
Based on the information provided:
- The row headings are: Row 1 = Coffee and Row 2 = Tea.
- The column headings for the snacks are: Column 1 = Cookies, Column 2 = Muffins, Column 3 = Scones.
The final table is:
[tex]$$
\begin{array}{|l|c|c|c|c|}
\hline
& \textbf{Cookies} & \textbf{Muffins} & \textbf{Scones} & \textbf{Total} \\
\hline
\textbf{Coffee} & 40 & 100 & 110 & 250 \\
\hline
\textbf{Tea} & 120 & 80 & 50 & 250 \\
\hline
\textbf{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
[tex]$$
\begin{array}{|c|c|c|c|c|}
\hline
& \,\,\,\,?\,\,\, & \,\,\,\,?\,\,\, & \,\,\,\,?\,\,\, & \text{Total} \\
\hline
\text{Row 1: } & 40 & 100 & 110 & 250 \\
\hline
\text{Row 2: } & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
We are given two pieces of information:
1. Approximately [tex]$36\%$[/tex] of the customers (of 500) buy a muffin.
2. Approximately [tex]$24\%$[/tex] of the tea drinkers have a scone with their tea.
Letβs use these facts step by step.
βββββββββββββββββββββββββββββββββββββββ
Step 1. Identify the Muffin Column
The total number of customers who buy a muffin is
[tex]$$0.36 \times 500 = 180.$$[/tex]
Looking at the column totals, the column that sums to 180 must correspond to muffins. Hence, the column with total 180 is for muffins.
βββββββββββββββββββββββββββββββββββββββ
Step 2. Assign Drinks (Rows)
The only two drinks are tea and coffee. The table shows two rows with equal totals of 250 customers each. One row corresponds to tea drinkers and the other to coffee drinkers. We will decide which row is tea by using the second piece of information.
βββββββββββββββββββββββββββββββββββββββ
Step 3. Match the Tea-Scone Information
We are told that approximately [tex]$24\%$[/tex] of the tea customers have a scone. Since there are 250 tea customers, we would ideally have
[tex]$$0.24 \times 250 = 60$$[/tex]
tea customers ordering scones. Inspect the two rows in the column βsconesβ (the column that is not yet assigned). The two values available in the unassigned scone column are [tex]$110$[/tex] and [tex]$50$[/tex]. No cell exactly gives 60, but the count [tex]$50$[/tex] is closer to the desired value (and within the range of approximation given the circumstances).
Thus, we assign the row containing [tex]$50$[/tex] in the scone column as the tea row. Consequently, the other row (with [tex]$110$[/tex] in the scone column) is the coffee row.
βββββββββββββββββββββββββββββββββββββββ
Step 4. Assign the Remaining Snack Columns
We already have:
- The column with total [tex]$180$[/tex] is muffins.
Now, the remaining two snack columns (with totals [tex]$160$[/tex] each) must be assigned among cookies and scones. Since we already determined from Step 3 that in the tea row the scone count is [tex]$50$[/tex], we choose the column that provides this [tex]$50$[/tex] for tea as the scone column. That leaves the other column (with total [tex]$160$[/tex]) to be cookies.
βββββββββββββββββββββββββββββββββββββββ
Step 5. Write the Final Table with Headings
The final assigned headings are:
- Drinks (rows):
- Row 1: Coffee
- Row 2: Tea
- Snacks (columns):
- Column 1: Cookies (total = 160)
- Column 2: Muffins (total = 180)
- Column 3: Scones (total = 160)
Thus, the completed table is:
[tex]$$
\begin{array}{|l|c|c|c|c|}
\hline
& \textbf{Cookies} & \textbf{Muffins} & \textbf{Scones} & \textbf{Total} \\
\hline
\textbf{Coffee} & 40 & 100 & 110 & 250 \\
\hline
\textbf{Tea} & 120 & 80 & 50 & 250 \\
\hline
\textbf{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
βββββββββββββββββββββββββββββββββββββββ
Step 6. Check the Conditions
1. Muffins: The muffin column total is [tex]$180$[/tex], which is exactly [tex]$36\%$[/tex] of 500 since [tex]$$\frac{180}{500} \times 100 = 36\%.$$[/tex]
2. Tea with scones: In the tea row, the scone count is [tex]$50$[/tex]. This is approximately [tex]$$\frac{50}{250} \times 100 = 20\%.$$[/tex]
Although [tex]$20\%$[/tex] is not exactly [tex]$24\%$[/tex], [tex]$50$[/tex] is the closest available value from the survey that can be assigned.
βββββββββββββββββββββββββββββββββββββββ
Conclusion
Based on the information provided:
- The row headings are: Row 1 = Coffee and Row 2 = Tea.
- The column headings for the snacks are: Column 1 = Cookies, Column 2 = Muffins, Column 3 = Scones.
The final table is:
[tex]$$
\begin{array}{|l|c|c|c|c|}
\hline
& \textbf{Cookies} & \textbf{Muffins} & \textbf{Scones} & \textbf{Total} \\
\hline
\textbf{Coffee} & 40 & 100 & 110 & 250 \\
\hline
\textbf{Tea} & 120 & 80 & 50 & 250 \\
\hline
\textbf{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
Thank you for reading the article A local cafΓ© serves tea coffee cookies scones and muffins They recently gathered data about their customers who purchase both a drink and a snack. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
