7-4 Two-Way Frequency Tables Objectives • Interpret data using a two-way frequency table
7 -4
Feb 17, 2016
7 -4. Two-Way Frequency Tables. Objectives Interpret data using a two-way frequency table. Suppose you asked 20 children and adults whether they liked broccoli. The table shows the data. - PowerPoint PPT Presentation
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7-4 Two-Way Frequency Tables
Objectives
• Interpret data using a two-way frequency table
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.
Yes NoChildren 3 8
Adults 7 2
Yes No TotalChildren 3 8 11
Adults 7 2 9
Total 10 10 20
Convert the table data to percentages
Yes No TotalChildren 3 8 11
Adults 7 2 9
Total 10 10 20
Yes No TotalChildren = .15 = 0.4 .55
Adults = .35 = 0.1 .45
Total 0.5 0.5 1.0
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%
Yes No TotalChildren = .15 = 0.4 .55
Adults = .35 = 0.1 .45
Total 0.5 0.5 1.0
Example 1Students in 9th and 10th grade are each asked which pet they prefer. Their responses are in the table below.
Grade Bird Cat Dog Fish Total9th 3 49 53 22 12710th 7 36 64 10 117Total 10 85 117 32 244
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
Grade Bird Cat Dog Fish Total9th 3 49 53 22 12710th 7 36 64 10 117Total 10 85 117 32 244
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
Grade Bird Cat Dog Fish Total9th 3 49 53 22 12710th 7 36 64 10 117Total 10 85 117 32 244
Example 2The table shows the amount of time students studied and the score each students earned on a recent test.
Hours spent studying 20–39 40–59 60–79 80–100 Total0–2 2 8 12 2 242–4 0 10 8 24 424–6 1 0 2 9 126+ 0 0 1 4 5
Total 3 18 23 39 83
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
Hours spent studying 20–39 40–59 60–79 80–100 Total0–2 2 8 12 2 242–4 0 10 8 24 424–6 1 0 2 9 126+ 0 0 1 4 5
Total 3 18 23 39 83
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
Hours spent studying 20–39 40–59 60–79 80–100 Total0–2 2 8 12 2 242–4 0 10 8 24 424–6 1 0 2 9 126+ 0 0 1 4 5
Total 3 18 23 39 83
Example 3100 students were asked which sport they prefer. Their responses are in the table below.
Group Baseball Basketball Soccer Football TotalBoys .16 .23 .15 .46 1.00Girls .06 .39 .36 .19 1.00Total .22 .62 .51 .65 2.00
Example 3 continued100 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%
Group Baseball Basketball Soccer Football TotalBoys .16 .23 .15 .46 1.00Girls .06 .39 .36 .19 1.00Total .22 .62 .51 .65 2.00
Example 3 continued100 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 sportsFalse
Group Baseball Basketball Soccer Football TotalBoys .16 .23 .15 .46 1.00Girls .06 .39 .36 .19 1.00Total .22 .62 .51 .65 2.00
Classwork/Homework
7-4 Worksheet
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