Let’s go through the steps to convert the given frequency table into a relative frequency table that uses decimals, and then into a relative frequency table that uses percentages.
### Step 1: Convert the Frequency Table to a Relative Frequency Table Using Decimals
From the given frequency table:
- The total number of customers surveyed is 80.
- Number of customers who prefer cheese: 22.
- Number of customers who prefer pepperoni: 34.
- Number of customers who prefer veggie: 24.
To find the relative frequency in decimals, we divide each category's frequency by the total number of customers.
Relative frequency (decimal) for Cheese:
[tex]\[ \text{Relative Frequency (Cheese)} = \frac{\text{Frequency (Cheese)}}{\text{Total Frequency}} = \frac{22}{80} = 0.275\][/tex]
Relative frequency (decimal) for Pepperoni:
[tex]\[ \text{Relative Frequency (Pepperoni)} = \frac{\text{Frequency (Pepperoni)}}{\text{Total Frequency}} = \frac{34}{80} = 0.425\][/tex]
Relative frequency (decimal) for Veggie:
[tex]\[ \text{Relative Frequency (Veggie)} = \frac{\text{Frequency (Veggie)}}{\text{Total Frequency}} = \frac{24}{80} = 0.3\][/tex]
Now, complete the table for relative frequency in decimals:
[tex]\[
\begin{tabular}{|l|c|c|c|c|}
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & \multicolumn{3}{|c|}{Preferred Toppings} \\
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Cheese & Pepperoni & Veggie & Total \\
\hline
\begin{tabular}{l}
Relative \\
Frequency \\
(decimals)
\end{tabular}
& 0.275 & 0.425 & 0.3 & 1.0 \\
\hline
\end{tabular}
\][/tex]
### Step 2: Convert the Frequency Table to a Relative Frequency Table Using Percentages
To convert the relative frequencies from decimals to percentages, we multiply each decimal by 100.
Relative frequency (percentage) for Cheese:
[tex]\[ \text{Percent Frequency (Cheese)} = 0.275 \times 100 = 27.5\% \][/tex]
Relative frequency (percentage) for Pepperoni:
[tex]\[ \text{Percent Frequency (Pepperoni)} = 0.425 \times 100 = 42.5\% \][/tex]
Relative frequency (percentage) for Veggie:
[tex]\[ \text{Percent Frequency (Veggie)} = 0.3 \times 100 = 30.0\% \][/tex]
Now, complete the table for relative frequency in percentages:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & \multicolumn{3}{|c|}{Preferred Toppings} \\
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Cheese & Pepperoni & Veggie & Total \\
\hline
\begin{tabular}{l}
Relative \\
Frequency \\
(percent)
\end{tabular}
& 27.5\% & 42.5\% & 30.0\% & 100\% \\
\hline
\end{tabular}
\][/tex]
By following these steps, we have successfully converted the frequency table of customer toppings preferences into both relative frequency tables using decimals and percentages.
