Two Way Tables

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Two way tables are used to display information. They can be used to find probabilities too. The two way table below shows information about the methods people go to school.

Walk Bus Train Car Total
Boy 290 131 52 101 574
Girl 408 49 13 144 614
Teacher 2 1 5 32 40
Total 700 181 70 277 1228

Notice that the entries in each row add up to the total in the rightmost column, so that in the row labelled ‘Boy’, 290+131+52+101=584 and the entries in each column add up to the total given in the bottom row, so that fro the column labelled ‘Walk’, 290+408+2=700.

If we wanted to find the probability that a person picked at random was a boy who walked to school, we would divide the number of boys who walk to schools by the total number of people, obtaining

If we wanted to find the probability that a person picked at random travelled by car to school, we would divide the number of people who travelled by car by the total number of people, obtaining

If we had a partially completed table, we can often complete it using the fact that the rows add to give the rightmost entry and the columns add to give the entries in the bottom row. Suppose we have the partially completed table below.

Walk Bus Train Car Total
Boy 290 131 574
Girl 49 13 144
Teacher 2 32 40
Total 181 70 277

We complete the table by looking for rows or columns with single missing entries, one at a time, indicated in green.

Walk Bus Train Car Total
Boy 284 136 592
Girl 48 12 149 654
Teacher 2 6 32 46
Total 190 87 284
Walk Bus Train Car Total
Boy 284 136 592
Girl 48 12 149 654
Teacher 2 6 6 32 46
Total 190 87 284
Walk Bus Train Car Total
Boy 284 136 69 592
Girl 48 12 149 654
Teacher 2 6 6 32 46
Total 190 87 284
Walk Bus Train Car Total
Boy 284 136 69 103 592
Girl 48 12 149 654
Teacher 2 6 6 32 46
Total 190 87 284
Walk Bus Train Car Total
Boy 284 136 69 103 592
Girl 445 48 12 149 654
Teacher 2 6 6 32 46
Total 190 87 284
Walk Bus Train Car Total
Boy 284 136 69 103 592
Girl 445 48 12 149 654
Teacher 2 6 6 32 46
Total 731 190 87 284
Walk Bus Train Car Total
Boy 284 136 69 103 592
Girl 445 48 12 149 654
Teacher 2 6 6 32 46
Total 731 190 87 284 1292 

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