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A two-way table is a frequency table that displays data collected from one source that belongs to two different categories. One category of data is represented by rows and the other is represented by columns. We want to construct a two-way table for the given data and interpret the relative frequencies by column. To do so, we will follow four steps.
Let's do these things one at a time.
We can start by looking at the given Venn diagram.
We know that the diagram shows the number of students that exercise in different ways. Notice that some students jog, while others do aerobics. This information is enough to determine the appropriate column and row headers for our table.
Jogging | No Jogging | Total | |
---|---|---|---|
Aerobics | |||
No Aerobics | |||
Total |
Jogging | No Jogging | Total | |
---|---|---|---|
Aerobics | 8; | 13; | |
No Aerobics | 24; | 5; | |
Total |
Jogging | No Jogging | Total | |
---|---|---|---|
Aerobics | 8; | 13 | 21; |
No Aerobics | 24; | 5; | 29 |
Total | 32; | 18; |
Jogging | No Jogging | Total | |
---|---|---|---|
Aerobics | 8; | 13 | 21; |
No Aerobics | 24; | 5; | 29 |
Total | 32; | 18; | 50 |
To find the relative frequencies by column, we calculate the ratios of each value and the total in that column. We will round the results to the nearest hundredth.
Jogging | No Jogging | Total | |
---|---|---|---|
Aerobics | 8;328=0.25 | 13;1813≈0.72 | 21;5021=0.42 |
No Aerobics | 24;3224=0.75 | 5;185≈0.28 | 29;5029=0.58 |
Total | 32;3232=1.00 | 18;1818=1.00 | 50;5050=1.00 |
Looking at the relative frequencies, we can say that most of the students who jog do no aerobics. Most of the students who do not jog do aerobics.