Answer :
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.
### 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.
