Essential Question What are joint and marginal frequencies

Essential Question: What are joint and marginal frequencies? Standard: 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. ★

Introduction Information about people who are surveyed can be captured in two-way frequency tables. A two-way frequency table is a table of data that separates responses by a characteristic of the respondents. Type of response Type of characteristic Response 1 Response 2 Characteristic 1 a b Characteristic 2 c d

� 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 sample table, a, b, c, and d are each joint frequencies. Type of response Type of characteristic Response 1 Response 2 Characteristic 1 a b Characteristic 1 c d

� Marginal frequency is the total number of times a response was given, or 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 sample table, a + b would be the marginal frequency of people with Characteristic 1. Type of response Type of characteristic Response 1 Response 2 Characteristic 1 a b Characteristic 1 c d

� Marginal and Joint Frequencies for 2 -way Tables Example 1: Female Texter Non-Texter 10 4 Male What are the joint frequencies? 6 8 What are the marginal frequencies?

Let’s Try Together: Example 2: Elizabeth surveys 9 th, 10 th, and 11 th graders. Grade Hours Spent on Homework 0 -2 2 -4 More than 4 9 38 12 2 10 21 25 9 11 14 18 20

Worktime with partner 7 -10