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The frequency table shows the results of a survey comparing the number of beach towels sold for full price and at a discount during each of the three summer months.

Beach Towel Sales
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
& Full Price & Discounted & Total \\
\hline
Month 1 & 49 & 1 & 50 \\
\hline
Month 2 & 120 & 5 & 125 \\
\hline
Month 3 & 101 & 24 & 125 \\
\hline
Total & 270 & 30 & 300 \\
\hline
\end{tabular}

The store owner converts the frequency table to a conditional relative frequency table by row.

Beach Towel Sales (Conditional Relative Frequency)
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
\multicolumn{1}{c|}{} & Full Price & Discounted & Total \\
\hline
Month 1 & 0.98 & 0.02 & 1.0 \\
\hline
Month 2 & 0.96 & 0.04 & 1.0 \\
\hline
Month 3 & 0.81 & 0.19 & 1.0 \\
\hline
\end{tabular}


Sagot :

To convert a frequency table to a conditional relative frequency table by row, we need to find the relative frequency for each entry with respect to its row total. Let's go through the process step-by-step for each row in your table.

### Month 1:

Step 1: Identify the entries and the row total.
- Full Price: 49
- Discounted: 1
- Total: 50

Step 2: Calculate the relative frequencies for each entry.
- Full Price: \( \frac{49}{50} = 0.98 \)
- Discounted: \( \frac{1}{50} = 0.02 \)
- Total: \( \frac{50}{50} = 1.0 \)

So, the conditional relative frequencies for Month 1 are:
- Full Price: 0.98
- Discounted: 0.02
- Total: 1.0

### Month 2:

Step 1: Identify the entries and the row total.
- Full Price: 120
- Discounted: 5
- Total: 125

Step 2: Calculate the relative frequencies for each entry.
- Full Price: \( \frac{120}{125} = 0.96 \)
- Discounted: \( \frac{5}{125} = 0.04 \)
- Total: \( \frac{125}{125} = 1.0 \)

So, the conditional relative frequencies for Month 2 are:
- Full Price: 0.96
- Discounted: 0.04
- Total: 1.0

### Month 3:

Step 1: Identify the entries and the row total.
- Full Price: 101
- Discounted: 24
- Total: 125

Step 2: Calculate the relative frequencies for each entry.
- Full Price: \( \frac{101}{125} = 0.808 \)
- Discounted: \( \frac{24}{125} = 0.192 \)
- Total: \( \frac{125}{125} = 1.0 \)

So, the conditional relative frequencies for Month 3 are:
- Full Price: 0.808
- Discounted: 0.192
- Total: 1.0

### Consolidated Conditional Relative Frequency Table:
Now, compiling the calculated relative frequencies, we get:

[tex]\[ \begin{array}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & \text{Full Price} & \text{Discounted} & \text{Total} \\ \hline \text{Month 1} & 0.98 & 0.02 & 1.0 \\ \hline \text{Month 2} & 0.96 & 0.04 & 1.0 \\ \hline \text{Month 3} & 0.808 & 0.192 & 1.0 \\ \hline \end{array} \][/tex]

Thus, the store owner successfully converted the frequency table into a conditional relative frequency table by row. The entries now show the proportion of each category within the respective month’s total sales.