The 0.2 in the highlighted cell of the relative frequency table represents the proportion of customers who neither ordered an appetizer nor ordered a dessert.
Given the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Appetizer & No appetizer & Total \\
\hline Dessert & 0.1 & 0.3 & 0.4 \\
\hline No dessert & 0.2 & 0.4 & 0.6 \\
\hline Total & 0.3 & 0.7 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Let's break it down:
1. Rows and Columns: The table is divided into two main categories: whether the customer ordered a dessert and whether they ordered an appetizer.
- The columns divide the data based on whether the customer ordered an appetizer or not.
- The rows divide the data based on whether the customer ordered a dessert or not.
2. Cells: Each cell shows the relative frequency (proportion) of customers who fall into each combination of categories.
- For example, the first cell (0.1) represents customers who ordered both an appetizer and a dessert.
- The second cell (0.3) represents customers who did not order an appetizer but did order a dessert.
- The third cell (0.2 and highlighted) represents customers who did not order either an appetizer or a dessert.
- The fourth cell (0.4) represents customers who ordered an appetizer but did not order a dessert.
3. Sum of Rows and Columns: Each row and each column sums to the total proportion who meet that single condition.
- The sum of the first row (Dessert) is [tex]\(0.1 + 0.3 = 0.4\)[/tex].
- The sum of the second row (No dessert) is [tex]\(0.2 + 0.4 = 0.6\)[/tex].
- The sum of the first column (Appetizer) is [tex]\(0.1 + 0.2 = 0.3\)[/tex].
- The sum of the second column (No appetizer) is [tex]\(0.3 + 0.4 = 0.7\)[/tex].
Thus, the 0.2 in the highlighted cell specifically means that 20% of the customers neither ordered an appetizer nor ordered a dessert.
