2Understand 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
3: 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 -.
11How do you organize data of students with cell phones that also have MP3 players?
12Cell PhoneNo Cell PhoneTotalMP3PlayerHave cell phone and mp3 playerHave mp3 player onlyTotal with MP3 playerNo MP3 PlayerHave cell phone, but no mp3 playerHave no cell phone or mp3 playerTotal with no MP3 playerTotal with cell phoneTotal with no cell phoneTotal SampledA 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. .
13Cell PhoneNo Cell PhoneTotalMP3 PlayerNo MP3 PlayerWhen 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.
14Cell PhoneNo Cell PhoneTotalMP3 Player60960+9=69No MP3 Player873Now 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.
15Cell PhoneNo Cell PhoneTotalMP3 Player60969No MP3 Player73-60 =13873We 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.
16Cell PhoneNo Cell PhoneTotalMP3 Player60969No MP3 Player13813+8=2173Now we can sum the second row to get 21.
17Cell PhoneNo Cell PhoneTotalMP3 Player60969No MP3 Player13821739+8=17Next we can sum the 2nd column to get 17 people with no cell phone.
18Cell PhoneNo Cell PhoneTotalMP3 Player60969No MP3 Player13821731769+21= 73+17= 90Now 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.