warm up Below are examples of two way frequency tables. Based on the images, how would you define two way frequency tables? Jan 31 4:09 AM 1
EQ STANDARD Summarize, represent, and interpret data on two categorical and quantitative variables. MCC9 12.S.ID.5 Summarize categorical data for two categories in two way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. How can you construct and interpret two way frequency tables? Jan 31 4:09 AM 2
Working with Two Categorical and Quantitative Variables KEY TERMS 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 two way frequency table marginal frequency: the total number of times a specific response is given, or the total number of people with a given characteristic. Jan 8 1:26 PM 3
KEY TERMS trend: a pattern of behavior, usually observed over time or over multiple iterations two way 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. Jan 8 1:33 PM 4
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Information about people who are surveyed can be captured in two way frequency tables. A two way 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 give by people with each characteristic. The sum of all cells, a + b + c + d, is the total number of respondents. Two way 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 two way frequency table. Jan 8 1:40 PM 6
A joint frequency is the number of responses for a given characteristic. The entries in the cells of a two way 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 two way 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 Jan 8 1:42 PM 7
For you: What is the joint frequency of females who prefer basketball? of males who prefer baseball? Jan 9 8:43 AM 8
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SUMMARY & homework Make a table of joint and marginal frequencies. 1. 2. Jan 31 4:08 AM 14