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Two way Tables

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Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. SP.4

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: A relative frequency is the fraction or proportion of times an answer occurs. To find the relative frequencies, divide each frequency by the total number of students in the sample -.

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You need to make a table to show the comparisons: you are comparing those who like chocolate and those who like caramel. You will also include those who don’t

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**How do you organize data of students with cell phones that also have MP3 players?**

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Cell Phone No Cell Phone Total MP3 Player Have cell phone and mp3 player Have mp3 player only Total with MP3 player No MP3 Player Have cell phone, but no mp3 player Have no cell phone or mp3 player Total with no MP3 player Total with cell phone Total with no cell phone Total Sampled A two way table shows data that pertain to two different categories. This is an example of a two way table that could hold information about the number of students that have either cell phones, mp3 players, both, or none. The headers are on the top and the left. You would place the numbers that represent each scenario in the middle and then total the rows and columns. .

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Cell Phone No Cell Phone Total MP3 Player No MP3 Player When given a word problem, you should organize the data that is given in the two-way table. (Read problem). Since 73 students own a cell phone in total, we will put 73 in the total column. 60 of the cell phone owners also own a MP3 player, so we will list the 60 in the cell that corresponds to owning both. 9 students have no cell phone, but have a MP3 player, so we place a 9 in that cell. Lastly, we are told that there are 8 students who don’t own either device. We place the 8 in the appropriate cell.

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Cell Phone No Cell Phone Total MP3 Player 60 9 60+9=69 No MP3 Player 8 73 Now that we have filled in the information that we already know, we can use what we know about two-way tables to complete the rest of the table. The sum of the first row is 69.

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Cell Phone No Cell Phone Total MP3 Player 60 9 69 No MP3 Player 73-60 =13 8 73 We cannot sum the second row until we get a value of the number of students who have a cell phone, but no MP3 player. WE know that the sum of the cell phone owners is 73. We can subtract the 60 from the 73 to get 13 people with a cell phone and no MP3 player.

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Cell Phone No Cell Phone Total MP3 Player 60 9 69 No MP3 Player 13 8 13+8=21 73 Now we can sum the second row to get 21.

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Cell Phone No Cell Phone Total MP3 Player 60 9 69 No MP3 Player 13 8 21 73 9+8=17 Next we can sum the 2nd column to get 17 people with no cell phone.

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Cell Phone No Cell Phone Total MP3 Player 60 9 69 No MP3 Player 13 8 21 73 17 69+21= 73+17= 90 Now we need to confirm that the sum of the sum of the rows is the same as the sum of the sum of the columns. 69 plus 21 is 90 as well as 73 plus 17.

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Cell Phone No Cell Phone Total MP3 Player 60 9 69 No MP3 Player 13 8 21 73 17 90 We now have a completed two way table from our original verbal description.

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