Working with Two Categorical and Quantitative Variables
conditional relative frequency: the percentage of a joint frequency as compared to the total number of respondents, total number of people with a given characteristic, or the total number of times a specific response was given.
function: a relation of two variables where each input is assigned to one and only one output.
joint frequency: the number of times a specific response is given by people with a given characteristic; the cell values in a two­way frequency table
marginal frequency: the total number of times a specific response is given, or the total number of people with a given characteristic.
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trend: a pattern of behavior, usually observed over time or over multiple iterations
two­way frequency table: a table that divides responses into categories showing both a characteristic in the table rows and a characteristic in the table columns; values in cells are a count of the number of times each response was given by a respondent with a certain characteristic.
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Information about people who are surveyed can be captured in two­way frequency tables. A two­way frequency table is a table that separates responses by a characteristic of the respondents.
Each cell in the table contains a count of the people with a given characteristic who gave each response. For example, in the table above a, b, c, and d would each be counts for the responses given by people with each characteristic. The sum of all cells, a + b + c + d, is the total number of respondents. Two­way frequency tables help organize information and provide greater insight into features of a population being surveyed. A trend, or pattern in the data can be examined using a two­way frequency table.
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A joint frequency is the number of responses for a given characteristic. The entries in the cells of a two­way frequency table are joint frequencies. In the table a, b, c, and d are each joint frequencies. A marginal frequency is the total number of times a response was given, of the total number of respondents with a given characteristic. This is the sum of either a row or a column in a two­way frequency table. In the same table, a + b would be the marginal frequency of people with Characteristic 1.
A conditional relative frequency allows a comparison to be made for multiple responses in a single row, single column, or table. Relative frequencies are expressed as a percentage, usually written as a decimal. They are found by dividing the number of responses by either the total number of people who gave that response, the total number of people with a given characteristic, or the total number of respondents. In the sample table, is the relative frequence of Response 1 for the people with Characteristic 1
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For you: What is the joint frequency of females who prefer basketball? of males who prefer baseball?
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