Summarizing Data Using Two-Way Frequency Tables

1. Summarizing Data Using Two-Way Frequency Tables ~adapted from walch education

2. Two-way Frequency Table • A two-way frequency table is a table of data that separates responses by a characteristic of the respondents • A trend, or pattern in the data, can be examined using a two-way frequency table.

3. Key Terms: • 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. • A 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.

4. Also… • A conditional relative frequency expresses a number of responses as a percentage of the total number of respondents, the total number of people with a given characteristic, or the total number of times a specific response was given. • In the sample table, is the relative frequency of Response 1 for people with Characteristic 1.

5. Practice Problem Ms. Scanlon surveys her students about the time they spend studying. She creates a table showing the amount of time students studied and the score each student earned on a recent test.

6. Ms. Scanlon wants to understand the distribution of scores among all the students, and to get a sense of how students are performing and how much students are studying. Find the conditional relative frequencies as a percentage of the total number of students. • First, we must find the total number of students represented in the table by summing the joint frequencies… 83 students

7. Next, divide each joint frequency by the total number of students

8. Now we can represent the conditional relative frequencies in a new table.

9. ~ Ms. Dambreville Thanks For Watching!!!!