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Understanding Two-Way Frequency Tables: A Guide to Data Interpretation

This resource explains how to interpret data using two-way frequency tables. It demonstrates the concepts of joint and marginal relative frequency, illustrated through examples involving children's and adults' preferences for broccoli, students' pet preferences, and study habits affecting test scores. Learn how to convert table data into percentages and answer relevant questions about survey results. Master the interpretation of two-way frequency tables to enhance your data analysis skills in various contexts.

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Understanding Two-Way Frequency Tables: A Guide to Data Interpretation

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  1. 7-4 Two-Way Frequency Tables • Objectives • Interpret data using a two-way frequency table

  2. Suppose you asked 20 children and adults whether they liked broccoli. The table shows the data. Joint relative frequency is the portion of the data that falls on the intersection of two variables Marginal relative frequency is found by adding the joint relative frequencies in each row and column.

  3. Convert the table data to percentages

  4. Use the table data to questions What percentage of the people surveyed were adults? 45% Of the 20 people asked, what percentage were children that liked broccoli? 15%

  5. Example 1 Students in 9th and 10th grade are each asked which pet they prefer. Their responses are in the table below.

  6. Example 1 Continued How many students preferred birds and cats? 10 + 85 = 95 How many 9th grade students preferred cats and fish? 49 + 22 = 71

  7. Example 1 Continued How many students did not prefer fish? 244 – 32 = 212 How many more 9th grade students preferred cats and dogs, compared to 10th graders? (49 + 53) – (36 + 64) = 102 – 100 = 2

  8. Example 2 The table shows the amount of time students studied and the score each students earned on a recent test.

  9. Example 2 continued How many students received a B or higher? 39 How students passed that studied for 0 – 4 hours? 12 + 2 + 8 + 24 = 46

  10. Example 2 continued How long should you study to have the best chance of passing? 2 – 4 hours How many students studied more than 4 hours? 12 + 5 = 17

  11. Example 3 100 students were asked which sport they prefer. Their responses are in the table below.

  12. Example 3 continued 100 students were asked which sport they prefer. Their responses are in the table below. What percentage of boys prefer football and baseball? .16 + .46 = .62 = 62% How many students do not prefer soccer? 49%

  13. Example 3 continued 100 students were asked which sport they prefer. Their responses are in the table below. T or F 65% of students prefer football. True T or F Girls prefer soccer over all other sports False

  14. Classwork/Homework 7-4Worksheet

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