The table shows how students traveled to school and whether they arrived on time. <table><tr><th></th><th>On time</th><th>Late</th><th>Total</th></tr><tr><th>Bus</th><td>\(14\)</td><td>\(6\)</td><td>\(20\)</td></tr><tr><th>Walk</th><td>\(9\)</td><td>\(3\)</td><td>\(12\)</td></tr><tr><th>Total</th><td>\(23\)</td><td>\(9\)</td><td>\(32\)</td></tr></table> a) How many students walked and arrived late? b) How many students walked in total?

Complete the missing interior count. <table><tr><th></th><th>Uses the library</th><th>Does not use the library</th><th>Total</th></tr><tr><th>Grade \(7\)</th><td>\(18\)</td><td></td><td>\(30\)</td></tr><tr><th>Grade \(8\)</th><td>\(22\)</td><td>\(18\)</td><td>\(40\)</td></tr></table>

Ramon is planning a two-way table for two categorical variables: grade level (Grade 7 or Grade 8) and usual travel method (Walk, Bus, or Car). He considers two layouts: - Layout A: Grade 7 and Grade 8 are rows; Walk, Bus, and Car are columns. - Layout B: Walk, Bus, and Car are rows; Grade 7 and Grade 8 are columns. a) Which layouts are valid two-way-table organizations? b) In each layout, where would the count of Grade 8 students who usually ride the bus appear? c) Explain why switching the row and column variables does not change the paired data being summarized.

Maya proposes this layout for a survey of grade level and travel method: <table><tr><th></th><th>Bus</th><th>Grade \(8\)</th></tr><tr><th>Walk</th><td></td><td></td></tr><tr><th>Grade \(7\)</th><td></td><td></td></tr></table> Explain why this layout is not a valid two-way-table organization for the two variables. Describe how the row and column headings should be organized instead. You do not need to supply any counts.

A store sorts orders by pickup or delivery and by payment method. One order is delivered and paid for by card. In which cell does it belong? <table><tr><th>Order type</th><th>Cash</th><th>Card</th></tr><tr><th>Pickup</th><td> </td><td> </td></tr><tr><th>Delivery</th><td> </td><td> </td></tr></table>

A bicycle repair stand checks four bikes. Here are the pairs (bike type, fixed that day): Road, yes Mountain, yes Road, no Mountain, yes Complete a two-way table with bike type as rows and fixed that day (yes/no) as columns. Include all totals.

A garden center sells seed packets and small plants at the counter and online. How many plant purchases were made altogether? <table><tr><th></th><th>Seeds</th><th>Plants</th></tr><tr><th>Counter</th><td>\(6\)</td><td>\(8\)</td></tr><tr><th>Online</th><td>\(3\)</td><td>\(5\)</td></tr><tr><th>Total</th><td>\(9\)</td><td>\(\square\)</td></tr></table>

A school surveyed students about interest in mathematics and physics. The four interior counts are shown. <table><tr><th></th><th>Interested in mathematics</th><th>Not interested in mathematics</th><th>Total</th></tr><tr><th>Interested in physics</th><td>\(120\)</td><td>\(130\)</td><td></td></tr><tr><th>Not interested in physics</th><td>\(180\)</td><td>\(70\)</td><td></td></tr><tr><th>Total</th><td></td><td></td><td></td></tr></table> a) Complete all row, column, and grand totals. b) Explain what the counts \(120\) and \(70\) mean. c) How many students are interested in exactly one of the two subjects?

Twelve students recorded how they traveled to school and whether they arrived early or late: Bike–Early, Walk–Early, Bike–Late, Bus–Early, Walk–Late, Bike–Early, Bus–Late, Bike–Early, Walk–Early, Bus–Early, Bike–Late, Walk–Early. Construct a two-way table of counts with travel method as rows and arrival category as columns.

A school records lunch choice for students in two grades. The tally totals are: - Grade \(7\): \(14\) cafeteria meals, \(9\) packed lunches, \(7\) skipped lunches. - Grade \(8\): \(10\) cafeteria meals, \(12\) packed lunches, \(8\) skipped lunches. Construct a complete two-way table.

The classification tree shows \(60\) students first by grade and then by how they travel to school. Construct a complete two-way table with grade as rows and travel method as columns.

The table contains exactly one incorrect total. Identify and correct it. <table><tr><th></th><th>Returned</th><th>Kept</th><th>Total</th></tr><tr><th>Online</th><td>\(16\)</td><td>\(44\)</td><td>\(60\)</td></tr><tr><th>Store</th><td>\(9\)</td><td>\(31\)</td><td>\(40\)</td></tr><tr><th>Total</th><td>\(25\)</td><td>\(74\)</td><td>\(100\)</td></tr></table>

Each two-letter code gives a student’s campus and course format. The first letter is North \(N\) or South \(S\); the second is hybrid \(H\) or in-person \(I\). \(NH, SI, NH, NI, SH, NH, SI, NI, SH, NH, SH, SI, NH, NI, SH, NH\) Construct a two-way table of counts.

Talia tries to construct a table for \(50\) survey responses. The planned row totals are \(28\) and \(22\), but the planned column totals are \(31\) and \(20\). Can a valid two-way table have these totals? Explain.

A school surveys \(34\) Grade \(7\) students and \(26\) Grade \(8\) students about whether they prefer e-books or printed books. The number of Grade \(7\) students who prefer e-books equals the number of Grade \(8\) students who prefer printed books. Eighteen Grade \(7\) students prefer e-books. Construct the complete table.

An after-school program has the following club-choice counts: <table><tr><th></th><th>Robotics</th><th>Art</th></tr><tr><th>Grade \(7\)</th><td>\(12\)</td><td>\(8\)</td></tr><tr><th>Grade \(8\)</th><td>\(9\)</td><td>\(11\)</td></tr></table> Four new Grade \(7\) responses arrive: \(3\) choose robotics and \(1\) chooses art. Four new Grade \(8\) responses all choose art. Construct the updated table with totals.

A community garden surveys \(50\) residents from two neighborhoods about whether they compost. Complete the table, including all margins. <table><tr><th></th><th>Composts</th><th>Does not compost</th><th>Total</th></tr><tr><th>North</th><td>\(19\)</td><td>\(8\)</td><td></td></tr><tr><th>South</th><td>\(14\)</td><td></td><td></td></tr><tr><th>Total</th><td></td><td></td><td>\(50\)</td></tr></table>

Coach Ellis tracks equipment borrowed by the Red and Blue practice groups. She wrote down each request: <table><tr><th>Group</th><th>Equipment</th><th>Number borrowed</th></tr><tr><td>Red</td><td>Cones</td><td>\(6\)</td></tr><tr><td>Blue</td><td>Hurdles</td><td>\(8\)</td></tr><tr><td>Red</td><td>Hurdles</td><td>\(4\)</td></tr><tr><td>Blue</td><td>Cones</td><td>\(7\)</td></tr><tr><td>Red</td><td>Cones</td><td>\(5\)</td></tr><tr><td>Blue</td><td>Hurdles</td><td>\(5\)</td></tr></table> Make a two-way table of the total number borrowed, with practice group as rows and equipment as columns. Include totals.

A school survey has column totals of \(45\) students who prefer e-books and \(35\) who prefer printed books. Among Grade \(7\) students, \(19\) prefer e-books. Among Grade \(8\) students, \(12\) prefer printed books. Construct the full table.

Priya surveys \(40\) students about two categorical variables: pet type (dog, cat, or no pet) and usual homework location (home or library). She summarizes the results this way: <table><tr><th>Category</th><th>Count</th></tr><tr><td>Dog</td><td>\(18\)</td></tr><tr><td>Cat</td><td>\(12\)</td></tr><tr><td>No pet</td><td>\(10\)</td></tr><tr><td>Home</td><td>\(25\)</td></tr><tr><td>Library</td><td>\(15\)</td></tr></table> Explain why this is not a two-way table for the two variables. Describe a correct row-and-column organization, and state what additional information is needed to fill the interior cells.

Lakeview Middle School wants a two-way table with grade level as the columns. The proposed row categories are “Plays soccer” and “Plays basketball.” Some students play both sports, and some play neither. Are those two row categories valid categories of one row variable if every surveyed student must be counted in exactly one row? Explain. Give one valid set of row categories that keeps the sports information and places every student in exactly one row.

Table A summarizes campus and travel method. <table><tr><th></th><th>Bus</th><th>Walk</th></tr><tr><th>North</th><td>\(14\)</td><td>\(9\)</td></tr><tr><th>South</th><td>\(8\)</td><td>\(11\)</td></tr></table> Jordan transposes the table and proposes Table B. <table><tr><th></th><th>North</th><th>South</th></tr><tr><th>Bus</th><td>\(14\)</td><td>\(8\)</td></tr><tr><th>Walk</th><td>\(11\)</td><td>\(9\)</td></tr></table> Does Table B represent exactly the same paired data as Table A? If not, identify every interior count in Table B that is misplaced and state where each belongs.

A school records grade level and preferred device type. The next lesson will compare device preferences **within each grade** by calculating row relative frequencies. Which variable should be placed in the rows of the count table to make that later comparison direct? Which variable should be placed in the columns? Would the opposite orientation still be a valid two-way count table? Explain.

At a movie theater, six tickets are recorded by seat section and showtime: Balcony–Evening, Floor–Matinee, Floor–Evening, Balcony–Matinee, Floor–Evening, Balcony–Evening. A worker made the table below but counted one ticket twice. Find the incorrect count and give the correct table, including totals. <table><tr><th></th><th>Matinee</th><th>Evening</th></tr><tr><th>Balcony</th><td>\(1\)</td><td>\(3\)</td></tr><tr><th>Floor</th><td>\(1\)</td><td>\(2\)</td></tr></table>

Eight museum visitors record their ticket type and whether they used an audio guide: Adult–Yes, Child–No, Senior–Yes, Adult–No, Child–Yes, Adult–Yes, Senior–No, Child–No. Make a two-way table with ticket type as rows and audio guide (Yes/No) as columns. Include totals.

Ms. Patel surveys \(32\) students. Seven belong to an athletics club, \(15\) play esports at least once a week, and \(16\) do neither. Make a complete two-way table for athletics club membership and weekly esports participation. Include the totals.

A health survey of \(1000\) participants found that \(600\) exercise regularly, \(550\) eat a balanced diet, and \(400\) do both. a) Complete a two-way table of counts. b) How many participants do neither? c) How many do exactly one of the two activities?

A veterinary clinic surveyed \(200\) pet owners. Complete the table, then answer the questions. <table><tr><th></th><th>Owns a dog</th><th>Does not own a dog</th><th>Total</th></tr><tr><th>Owns a cat</th><td>\(30\)</td><td></td><td></td></tr><tr><th>Does not own a cat</th><td></td><td>\(55\)</td><td>\(110\)</td></tr><tr><th>Total</th><td>\(85\)</td><td></td><td>\(200\)</td></tr></table> a) Complete the two-way table. b) What do the counts \(30\) and \(55\) mean in context? c) How many respondents own at least one of the two pets?

A school surveyed \(25\) students about whether they play a musical instrument and whether they play a sport regularly. The survey found that \(12\) play an instrument, \(15\) play a sport regularly, and \(4\) do neither. a) Create a complete two-way table of counts. b) How many students do both activities? c) What percentage play a sport regularly but do not play an instrument?

An electronics store reviews \(200\) smartphones that were sold. Of the phones, \(120\) use Android, \(90\) were sold with a screen protector, and \(70\%\) of the Android phones were sold without a screen protector. a) Find the number of Android phones sold with a screen protector. b) Complete a two-way table for the data. c) How many non-Android phones were sold with a screen protector?

A quality-control team inspects \(1000\) components for a material defect and a shape defect. The team finds that: - \(920\) components do not have a material defect. - \(35\) components have a shape defect but no material defect. - \(20\) components have both defects. a) Complete a two-way table of counts. b) How many components have a shape defect? c) How many components have at most one of the two defects? Explain how you found the number.

A survey includes \(40\) students who play a musical instrument and \(50\) students who do not. The pie charts show club membership within each group. Panel a) is for students who play an instrument, and panel b) is for students who do not. Construct a complete two-way table of counts with instrument status as rows and club membership as columns.

A community center surveys \(38\) teens about chess club and art club. Nine belong to both clubs, \(7\) belong to neither, and \(22\) belong to exactly one club. Of those in exactly one club, \(13\) are in chess only. Construct a complete two-way table.

A robotics event has \(40\) first-time participants and \(40\) returning participants. Among first-time participants, \(60\%\) finish the challenge. Eighteen returning participants finish. Construct a complete table for participant type and completion.

A transit study first records three travel modes: <table><tr><th></th><th>Rain</th><th>No rain</th></tr><tr><th>Car</th><td>\(8\)</td><td>\(5\)</td></tr><tr><th>Bus</th><td>\(11\)</td><td>\(6\)</td></tr><tr><th>Walk</th><td>\(7\)</td><td>\(3\)</td></tr></table> Construct a new two-way table with rows “Car” and “Not car.” Include all totals.

At a museum workshop, \(45\) adults and \(30\) youths attend. Among adults, twice as many attend the morning session as the evening session. Altogether, \(46\) people attend in the morning. Construct a complete two-way table.

Three science classes each have \(20\) students. In Class A, \(12\) choose the lab option. In Class B, \(11\) choose the project option. Class C has \(5\) project students. Construct the complete table.

A survey receives \(70\) forms, but \(6\) forms omit one of the two categorical answers and are excluded from a two-way table. Of the usable forms, \(34\) are from Grade \(7\); \(22\) of those select “Yes.” Eighteen Grade \(8\) students select “Yes.” Construct the table for the usable responses.

A recreation center surveys \(40\) weekday visitors and \(50\) weekend visitors. Seventy percent of weekday visitors use the pool, while \(36\%\) of weekend visitors use it. Construct a complete table of counts.

A certification test has \(42\) morning examinees and \(30\) evening examinees. Two-thirds of the morning group pass, and \(43\) examinees pass altogether. Construct a complete table.

The counts are \(13\) urban bus riders, \(7\) urban train riders, \(5\) rural bus riders, and \(15\) rural train riders. Construct two equivalent tables: one with location as rows and one with transportation as rows.

A festival has \(40\) local visitors and \(45\) out-of-town visitors. Local visitors choose indoor and outdoor events in a ratio of \(3:2\). Out-of-town visitors choose indoor and outdoor events in a ratio of \(1:2\). Construct a complete two-way table.

A community center surveys \(30\) teen members and \(42\) adult members about whether they plan to volunteer. Altogether, \(36\) members answer “Yes,” and one-third of all “Yes” responses come from teens. Construct the complete table.

Three clubs each send \(20\) students to choose one of three sessions. Club A sends \(8\) to Coding and \(5\) to Design. Club B sends \(6\) to Coding and \(9\) to Design. Club C sends \(10\) to Coding and \(4\) to Design. Construct a complete \(3\times3\) two-way table including the Research session and all totals.

A school surveys \(100\) students about grade level and how they travel to school. Overall, \(30\%\) are Grade \(7\) students who ride the bus, \(18\%\) are Grade \(7\) students who walk, and \(12\%\) are Grade \(8\) students who ride the bus. Construct the complete count table.

A school lunch survey initially shows \(20\) Grade \(7\) cafeteria choices, \(10\) Grade \(7\) packed-lunch choices, \(14\) Grade \(8\) cafeteria choices, and \(16\) Grade \(8\) packed-lunch choices. One Grade \(7\) response was mistakenly entered as cafeteria instead of packed lunch. Construct the corrected table with totals.

Students rate a workshop after attending either online or in person: <table><tr><th></th><th>Agree</th><th>Maybe</th><th>Disagree</th></tr><tr><th>Online</th><td>\(12\)</td><td>\(5\)</td><td>\(3\)</td></tr><tr><th>In person</th><td>\(8\)</td><td>\(4\)</td><td>\(6\)</td></tr></table> Recode the responses into “Agree” and “Does not agree,” then construct the new table with totals.

A school surveys \(27\) Grade \(7\) students and \(33\) Grade \(8\) students about whether they will volunteer at a school event. The two grades have the same number of “Yes” responses, and there are \(34\) “No” responses altogether. Construct the table.

Three neighborhoods contribute \(25\), \(20\), and \(30\) responses to a transit survey. Across all neighborhoods, \(40\) residents prefer the bus. Neighborhood \(1\) has \(16\) bus responses, and Neighborhood \(2\) has \(9\). Construct the table.

Fifty devices are classified by location and condition. The records show \(18\) indoor-working, \(7\) indoor-needs-repair, \(12\) outdoor-working, and \(9\) outdoor-needs-repair devices. Four devices have condition “Not recorded,” split equally between locations. Construct a table with three condition columns.

The data list contains one accidental duplicate. Each entry is student ID–campus–travel method: 101–North–Bus, 102–North–Walk, 103–South–Walk, 104–North–Bus, 105–South–Bus, 104–North–Bus, 106–South–Walk, 107–North–Bus, 108–South–Walk. Remove the duplicate ID and construct the table.

A quality-control team checks \(50\) components for a material defect and a surface defect. Of the \(50\) components, \(28\) have a material defect and \(31\) have a surface defect. No other information is given. a) What is the smallest possible number of components that could have both defects? Construct a complete two-way table that shows this case. b) What is the largest possible number of components that could have both defects? Construct a complete two-way table that shows this case.

A library has \(34\) East Branch registrations and \(26\) West Branch registrations. There are \(35\) online registrations in all. At the East Branch, online registrations exceed in-person registrations by \(8\). Construct a complete two-way table.

A school records grade level and preferred workshop in this partial table. The two workshop column totals are equal. Find \(x\) and complete the table. <table><tr><th></th><th>Coding</th><th>Design</th><th>Total</th></tr><tr><th>Grade \(7\)</th><td>\(x\)</td><td>\(18\)</td><td></td></tr><tr><th>Grade \(8\)</th><td>\(26\)</td><td>\(2x\)</td><td></td></tr><tr><th>Total</th><td></td><td></td><td></td></tr></table>

A school knows that \(30\) Grade \(7\) students and \(20\) Grade \(8\) students were surveyed. It also knows that \(25\) students ride the bus and \(25\) walk. No interior count is given. Can the four grade-and-travel counts be determined uniquely? Give two different valid completions.

A community center surveys \(90\) members about whether they plan to volunteer. Teens make up \(40\%\) of the respondents. Overall, “Yes” and “No” responses are in a ratio of \(5:4\). Among teens, two-thirds answer “Yes.” Construct a complete table by age group and response.

An initial school travel table has North campus: \(10\) bus riders and \(14\) walkers; South campus: \(16\) bus riders and \(8\) walkers. One walker was assigned to North but belongs to South. Then one South campus student changes from bus to walking after the record is verified. Construct the final table.

A climbing gym recorded these 12 visits by day and session: Weekday–Morning, Weekend–Evening, Weekday–Evening, Weekend–Morning, Weekday–Morning, Weekend–Evening, Weekend–Evening, Weekday–Morning, Weekend–Morning, Weekday–Evening, Weekend–Evening, Weekday–Morning. A worker made the table below. Check it against the visit list. Make any corrections needed, including totals, and explain what the worker got wrong. <table><tr><th></th><th>Morning</th><th>Evening</th><th>Total</th></tr><tr><th>Weekday</th><td>\(3\)</td><td>\(3\)</td><td>\(6\)</td></tr><tr><th>Weekend</th><td>\(3\)</td><td>\(3\)</td><td>\(6\)</td></tr><tr><th>Total</th><td>\(6\)</td><td>\(6\)</td><td>\(12\)</td></tr></table>

At a museum gift shop, each receipt is for either one postcard or one book. The staff made this table: <table><tr><th></th><th>Cash</th><th>Card</th><th>Total</th></tr><tr><th>Postcard</th><td>\(12\)</td><td>\(8\)</td><td>\(20\)</td></tr><tr><th>Book</th><td>\(6\)</td><td>\(14\)</td><td>\(20\)</td></tr><tr><th>Total</th><td>\(18\)</td><td>\(22\)</td><td>\(40\)</td></tr></table> Then the staff found three mistakes: - Two book purchases paid in cash had been counted as postcards paid in cash. - Three postcard purchases paid by card had each been counted twice. - One book purchase paid by card had not been counted. Make the corrected two-way table, including totals. Which corrections change the table's grand total?