Two-Way Tables

Use the row and column named in the question.

Use the total for the Tuesday row.

Find the Salad column total.

Use either the two row totals or the two column totals.

Work across the row with one missing count.

Use the Tea column total.

1. The Tea column totals 31. Subtract the 14 morning tea customers: x=31-14=17.

Subtract the known row total from the grand total.

1. There are 70 people altogether, of whom 32 are in Group A. Group B has 70-32=38.
2. Check: 15+23=38.

Use only the girls’ total and girls’ bus count.

1. The 19 girls are split between bus and walking. Girls walking: 19-11=8.

The choice is from the whole table.

1. The bus column total is 30 and the grand total is 50.
2. The probability is \frac{30}{50}=\frac35.

Use the intersection cell for the numerator.

1. The Year 8 and Walk cell contains 8 students. The choice is from all 50.
2. The probability is \frac8{50}=\frac4{25}.

Find a row or column with only one missing number first.

Part (a)

1. x=30-18=12.

Part (b)

1. y=30-18=12, using the Swim column total.

Part (c)

1. z=12+14=26. Check with the grand total: 56-30=26.

The chosen person is already known to be a cyclist.

1. The choice is only from the Cycle column, which has 20 people. Eight are afternoon cyclists.
2. The probability is \frac8{20}=\frac25.

The percentage is of girls, so use their row total.

1. There are 18 school-meal users out of 30 girls.
2. \frac{18}{30}\times100=60\%.

Place each given fact in its correct row and column, then use the totals.

Part (a)

1. The x cell is adults choosing comedy. The question gives 25 adults who choose comedy, so x=25.

Part (b)

1. There are 80-45=35 children. Twelve choose comedy, so y=35-12=23 children choose drama.

Part (c)

1. Adults choosing drama: 45-25=20. Children choosing drama: 23.
2. The drama total is z=20+23=43. Check: comedy total 25+12=37, and 37+43=80.

Use the percentage to fill the boys’ school-meal cell first.

1. Boys taking school meals: 0.60\times40=24, so boys with packed lunches: 40-24=16.
2. Girls with packed lunches: 30-18=12. The total with packed lunches is 16+12=28.

Find the adults’ walking count before using the walking total.

1. Adults who walked: 48-18-20=10.
2. Children who walked: 24-10=14. Check: children by car 32-18=14 and by bus 28-20=8; 14+8+14=36.

Compare attendance as a fraction of each club’s total.

Part (a)

1. \frac{18}{30}\times100=60\%.

Part (b)

1. \frac{21}{42}\times100=50\%.

Part (c)

1. Club A has 60% attendance and Club B has 50%. Club A has the greater attendance percentage despite having fewer attendees.

Update the two affected cells, then select the correct group total.

1. Year 9 cyclists increase to 12+4=16. Year 10 still has 8 cyclists, so the new cycling total is 16+8=24.
2. The probability is \frac{16}{24}=\frac23. The grand total stays 50, but only cyclists are eligible for this choice.

A person who attends both belongs in just one intersection cell.

Part (a)

1. Music only: 45-18=27. Sport only: 42-18=24.
2. The number in at least one club is 18+27+24=69. Neither: 90-69=21.

Part (b)

1. There are 21 in neither club out of 90: \frac{21}{90}=\frac7{30}.

Use the probability to recover the library column total first.

1. The 18 girls using the library represent 3 of 5 equal parts. One part is 18\div3=6, so the library total is 5\times6=30.
2. Boys using the library: 30-18=12. There are 24 boys altogether, so boys not using it: 24-12=12.