Conditional Relative Frequencies In Exercises 37–42, use the contingency table from Exercises 33–36, and the information below.
Relative frequencies can also be calculated based on the row totals (by dividing each row entry by the row’s total) or the column totals (by dividing each column entry by the column’s total). These frequencies are conditional relative frequencies and can be used to determine whether an association exists between two categories in a contingency table.


What percent of U.S. adults ages 25 and over who are employed have a degree?

Verified step by step guidance

1. Step 1: Understand the problem. You are tasked with calculating the conditional relative frequency of U.S. adults ages 25 and over who are employed and have a degree. This involves using a contingency table and dividing the relevant frequency by the appropriate total.
2. Step 2: Identify the relevant row or column in the contingency table. Locate the row or column that corresponds to 'employed' and 'have a degree.' Ensure you have the frequency value for this specific category.
3. Step 3: Determine the total for the row or column. If you are calculating based on the row totals, sum all the entries in the row corresponding to 'employed.' If you are calculating based on the column totals, sum all the entries in the column corresponding to 'have a degree.'
4. Step 4: Calculate the conditional relative frequency. Divide the frequency of U.S. adults who are employed and have a degree by the total for the row or column you identified. Use the formula: $\frac{\mathrm{Frequency}}{\mathrm{Total}}$
5. Step 5: Convert the result into a percentage. Multiply the conditional relative frequency by 100 to express it as a percentage. The formula is: $\mathrm{Percentage}=\frac{\mathrm{Frequency}}{\mathrm{Total}}\times 100$

Key Concepts

Contingency Table

A contingency table is a type of data representation that displays the frequency distribution of variables. It allows for the examination of the relationship between two categorical variables by showing how the frequencies of one variable are distributed across the categories of another. Each cell in the table represents the count of occurrences for a specific combination of categories, facilitating the analysis of potential associations.

Relative Frequency

Relative frequency is a statistical measure that expresses the frequency of a particular category as a proportion of the total number of observations. It is calculated by dividing the count of occurrences in a category by the total number of observations. This concept is crucial for understanding the distribution of data and allows for comparisons between different categories, especially in the context of conditional probabilities.

Conditional Probability

Conditional probability refers to the likelihood of an event occurring given that another event has already occurred. In the context of a contingency table, it helps to determine the probability of one category based on the presence of another category. This concept is essential for analyzing associations between variables, as it provides insights into how the occurrence of one variable affects the probability of another.