16 Two-Way Tables - Glencoe

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Lesson16Main IdeaConstruct and interprettwo-way tables.Two-Way TablesSCHOOL The data from a survey of 50 students is shown in theVenn diagram. The students were asked whether or not theywere taking a foreign language and whether or not theyplayed a sport.ForeignLanguageNew VocabularySporttwo-way tablerelative frequency23Math Online1410glencoe.com38.SP.41. How many students are taking a foreign language?2. How many students play a sport?3. How many students do both?4. How many students do not play a sport and do not take a foreignlanguage?5. How many students play a sport but do not take a foreignlanguage?A two-way table is similar to a Venn diagram. A two-way tableshows data that pertain to two different categories. The datafrom one sample group is shown as it relates to twodifferent categories.The same information from the Venn diagram above is shownbelow as a two-way table, where one category is representedby rows and the other category is represented by columns.Play a SportDo Not Play a SportTotalTake a ForeignLanguage142314 23 or 37Do Not Take aForeign Language10310 3 or 1314 10 or 2423 3 or 2650TotalThe totals shown are for the corresponding row or column with agrand total of 50 students in the data set.In this lesson, you will learn how to construct and analyze two-waytables from words and diagrams.Lesson 16 Two-Way Tables67

Construct a Two-Way TableTECHNOLOGY Felipe surveyed students at his school. He foundthat 78 students own a cell phone and 57 of those students ownan MP3 player. There are 13 students that do not own acell phone, but own an MP3 player. Nine students do notown either device. Construct a two-way table summarizingthe data.Step 1Create a table using the two categories: cell phones andMP3 players.MP3 PlayerNo MP3 PlayerTotalCell PhoneNo Cell PhoneTotalStep 2Use the values given to fill in the table.MP3 PlayerCell Phone57No Cell Phone13No MP3 PlayerTotal789TotalStep 3Use reasoning to complete the table. Remember, the totalsare for each row and column. The column labeled “Total”should have the same sum as the row labeled “Total.”MP3 PlayerNo MP3 PlayerTotalCell Phone572178No Cell Phone13922Total7030100a. SUMMER CAMP There are 150 children at summer camp and71 signed up for swimming. There were a total of 62 childrenthat signed up for canoeing and 28 of them also signed up forswimming. Construct a two-way table summarizing the data.Real-World LinkRTThere are about12,000 summercamps across theUnited States.A two-way table can also show relative frequencies. Relativefrequency is the ratio of the value of a subtotal to the value of thetotal. In Example 1, the relative frequency of students who own a cell57phone who also own an MP3 player isor about 0.73.785778number of students who own a cell phone and an MP3 playertotal number of studentsA two-way table can show relative frequencies for rows or forcolumns, rather than the actual values.

Relative Frequencies in a Two-Way TableSCHOOL Using the two-way table from the beginning of thelesson, find the relative frequencies by row and then by column.What is the relative frequency of students that take a foreignlanguage and play a sport to all students taking a foreignlanguage?To find the relative frequencies by row, write the ratios of each valueto the total in that row. Round to the nearest hundredth if necessary.Frequency by RowWhen the numerator anddenominator of a fractionare equal, the decimalequivalent is 1.00.Play a SportDo Not Play a SportTotalTake a ForeignLanguage14 0.3823 0.621.00Do Not Take aForeign Language10 0.773 0.231.00Total24 0.4826 0.521.0037135037135014The relative frequency isor about 0.38.37What is the relative frequency of students that neither play asport nor take a foreign language to all students that do notplay a sport?When creating a two-way table with relative frequencies bycolumn, use the total of the columns when writing the ratios.Frequency by ColumnPlay a SportDo Not Play a SportTotalTake a ForeignLanguage14 0.5823 0.8837 0.74Do Not Take a ForeignLanguage10 0.423 0.1213 0.261.001.001.00Total2424262650503The relative frequency isor about 0.12.26b. TRAVEL A class was surveyed about whether they have been toCanada or Mexico. Find the relative frequencies by row andthen by column for the two-way table shown. Round to thenearest hundredth if necessary. What is the relative frequency ofa student who has been to both Canada and Mexico to allstudents that have been to Mexico?Have Been toCanadaHave Not Been toCanadaTotalHave Been to Mexico639Have Not Been to Mexico51116Total111425

Example 1Use the information to construct a two-way table.1. SURVEY Eloise surveyed the students in her cafeteria and found that38 males agree with the new cafeteria rules while 70 do not. There were92 females surveyed and 41 of them agree with the new cafeteria rules.Examples 2 and 32. NEWS The two-way table shows how some students get their news.TVInternetgrade13498th grade20687tha. How many students were surveyed?b. What is the relative frequency of students that responded TV to thetotal number of students surveyed? Round to the nearest hundredthif necessary.c. Do a higher percent of 7th graders or 8th graders get their news fromthe Internet? Justify your response.Use the information to construct a two-way table.Example 13. FOOD There were 100 customers in a restaurant that were asked whetherthey liked chicken or beef and whether they liked rice or pasta. Out of30 customers that liked rice, 20 liked chicken. There were 60 customersthat liked chicken.4. MOVIES As each person entered the theater, Aaron counted how manyof the 105 people had popcorn and how many had a drink. He foundthat out of 84 people that had popcorn, only 10 did not have a drink.Six people walked in without popcorn or a drink.Examples 2 and 35. ALLOWANCE The two-way tableshows the number of studentsthat do or do not do chores athome and whether they receivean allowance or not.AllowanceNo AllowanceDo Chores133Do Not DoChores54a. How many total students do chores?b. What is the relative frequency of students that do chores and get anallowance to the number of students that do chores? Round to thenearest hundredth if necessary.c. What is the relative frequency of students that do not do chores norget an allowance to the total number of students? Round to the nearesthundredth if necessary.

6. SCHOOL The two-way table showsthe number of Sasha’s soccerteammates that are in her Math classand English class.a. How many teammates doesSasha have?Math ClassNot in MathClassEnglish Class42Not inEnglish Class13b. What is the relative frequency of teammates that are in both of Sasha’sclasses to all of her teammates?c. Of the teammates in her math class, which percentage is higher: thepercentage of teammates that are in her English class or the percentageof teammates that are not in her English class?B7. MESSAGING The results of a survey showthe number of 7th graders and thenumber of 8th graders that message ona daily basis. Find the relativefrequencies by row and then bycolumn. Round to the nearesthundredth if necessary.8. VOLUNTEERING The two-way table showsthe places that males and femalesvolunteered in the past month. Do ahigher percentage of males or femalesvolunteer at the animal shelter? Justifyyour response.Real-World LinkRA total of 63.4 millionvolunteers contributed8.1 billion hours ofservice in 2009.9. EXERCISE The Venn diagram shows thenumber of students that exercise indifferent ways. Construct a two-waytable that displays the data. What isthe relative frequency of the numberof students that jog and do aerobicsto the total number of students? Roundto the nearest hundredth if necessary.TextMessageInstantMessage7th graders46388th5941gradersMalesFemalesAnimal 813510. LUNCH Cali surveyed the students inNumber ofMalesFemalesthe cafeteria about the number of timesTimes per Monththey bring their lunch to school per0– 53525month. The table shows her findings.23166–10Construct a two-way table that shows221311–15the relative frequencies by columns.18816–20What is the relative frequency of thenumber of girls that bring their lunch to school less than 6 times a monthto the total number of students surveyed? Round to the nearesthundredth if necessary.Lesson 16 Two-Way Tables71

C11. OPEN ENDED Survey your classmates to find out what kinds of afterschool jobs they prefer. Make a two-way table that displays yourresults.12. CHALLENGE The two-way table below shows the number of studentswith each hair color and eye color.Eye ColorHair Hazel25119Green13127Total122871360Which is greater: the percentage of the brown-haired students with blueeyes or the percentage of the red-haired students with brown eyes?13. WRITE MATH Refer to Example 2. Explain how to find the relativefrequency of students that do not take a foreign language but play asport to the students that do not take a foreign language.TTest Practice14. The two-way table below shows thenumber of hours students studied andwhether they studied independently orwith a study group.Studied LessThan 2 HoursStudied MoreThan 2 HoursStudiedIndependently124Studied with aStudy Group811What is the relative frequency ofstudents that studied independently formore than 2 hours to the total number ofstudents that studied independently?A. 0.4B. 0.33C. 0.25D. 0.1115.SHORT RESPONSE The Pep Club wasasked to vote for which dinner theywould like for their banquet. Construct atwo-way table for the informationshown in the Venn diagram below.Lasagna19Tacos13115

A two-way table is similar to a Venn diagram. A two-way table shows data that pertain to two different categories. The data from one sample group is shown as it relates to two . Canada or Mexico. Find the relative frequencies by row and then by column for the two-way table shown. Round to the

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