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 have a degree are not in the civilian labor force?

Verified step by step guidance

1. Step 1: Identify the relevant data from the contingency table. Locate the row corresponding to U.S. adults ages 25 and over who have a degree and the column corresponding to those not in the civilian labor force.
2. Step 2: Find the total number of U.S. adults ages 25 and over who have a degree (row total). This will be used as the denominator for calculating the conditional relative frequency.
3. Step 3: Extract the specific value from the contingency table that represents the number of U.S. adults ages 25 and over who have a degree and are not in the civilian labor force. This will be the numerator for the calculation.
4. Step 4: Calculate the conditional relative frequency by dividing the numerator (number of individuals with a degree not in the civilian labor force) by the denominator (total number of individuals with a degree). Use the formula: $\frac{\mathrm{Numerator}}{\mathrm{Denominator}}$
5. Step 5: Convert the conditional relative frequency into a percentage by multiplying the result by 100. Use the formula: $\mathrm{Percentage}=\frac{\mathrm{Numerator}}{\mathrm{Denominator}}\times \; 100$

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 event or category as a proportion of the total number of observations. It is calculated by dividing the count of occurrences of a specific category by the total number of observations. This concept is crucial for understanding the distribution of data and making comparisons between different categories within a dataset.

Conditional Relative Frequency

Conditional relative frequency refers to the relative frequency of a category given a specific condition or subset of data. It is calculated by dividing the frequency of a particular category by the total frequency of the condition being considered, such as row or column totals in a contingency table. This concept helps in assessing the relationship between two categorical variables and determining if an association exists.