Frequency Trees

Follow the child branch, then the cannot swim branch.

The numbers on the two first branches add up to the total.

The two branches coming out of a box add up to the number in that box.

Each pair of branches adds up to the number in the box they come from.

Tea appears on two branches: one for men and one for women.

The two branches from the female box add up to the number in that box.

1. There are 38 females.
2. 9 of the females did not have breakfast.
3. 38-9=29 females had breakfast.

First work out how many students do not come by bus.

1. Students who do not come by bus: 75-40=35.
2. 12 of these 35 students have school dinners.
3. 35-12=23 do not come by bus and do not have school dinners.

The yes boxes for men and for women add up to the total number who said yes.

Part (a)

1. 25 men said yes.
2. 56-25=31 women said yes.

Part (b)

1. There are 50 women and 31 of them said yes.
2. 50-31=19 women said no.

Find the right box at the end of the tree, then write it over the total.

1. Follow the branch 30 or over, then do not swim: 24 members.
2. As a fraction of 60: \frac{24}{60}.
3. Divide top and bottom by 12: \frac{24}{60}=\frac{2}{5}.

Probability = number of people in the right box ÷ total number of people.

1. Children who bought a programme: 5.
2. There are 50 people altogether.
3. Probability =\frac{5}{50}=\frac{1}{10}.

Put each piece of information in its box first, then use the fact that each pair of branches adds up to the box it comes from.

Part (a)

1. The other 90-50=40 people were children.

Part (b)

1. 50 adults, 32 of them bought popcorn.
2. 50-32=18 adults did not buy popcorn.

Part (c)

1. 40 children, 15 of them did not buy popcorn.
2. 40-15=25 children bought popcorn.

Read each sentence carefully: is it about all the students, one year group, or one year group who play?

Part (a)

1. 14 is the number of Year 11 students who play an instrument.
2. Follow Year 11 (box Q), then yes: that is box T.

Part (b)

1. Box R is Year 10 students who play.
2. 65 Year 10 students and 38 do not play.
3. 65-38=27.

Part (c)

1. Year 11 students: 120-65=55.
2. 14 of them play, so 55-14=41 do not play.

People who went on holiday appear on two branches: men and women.

1. Men who went on holiday: 28. Women who went on holiday: 36.
2. 28+36=64 people went on holiday.
3. Probability =\frac{64}{100}=\frac{16}{25} (or 0.64).

The girl is chosen from the girls only, so the bottom of your fraction is the number of girls.

1. There are 64 girls.
2. 16 of the girls failed.
3. Probability =\frac{16}{64}=\frac{1}{4}.

Compare fractions of each group, not just the numbers who passed.

Part (a)

1. 24 of the 40 adults passed.
2. \frac{24}{40}=\frac{3}{5}.

Part (b)

1. 21 of the 30 children passed.
2. \frac{21}{30}=\frac{7}{10}.

Part (c)

1. \frac{3}{5}=\frac{6}{10}, which is less than \frac{7}{10}.
2. A greater fraction of the children passed, so the children did better.

The 70 people on a tour are made up of adults on a tour and children on a tour.

Part (a)

1. 70 people went on a tour and 23 of them were children.
2. Adults on a tour: 70-23=47.

Part (b)

1. 84 adults and 47 went on a tour.
2. 84-47=37 adults did not go on a tour.

Part (c)

1. Children: 150-84=66.
2. 66-23=43 children did not go on a tour.

Start by working out \frac{5}{8} of 160.

Part (a)

1. 160\div8=20, so \frac{1}{8} of 160 is 20.
2. \frac{5}{8} of 160 is 5\times20=100.

Part (b)

1. People aged 25 or over: 160-100=60.
2. 33 of them failed, so 60-33=27 passed.

Part (c)

1. Under 25 passed: 62. 25 or over passed: 27.
2. 62+27=89.

Decide who the person is chosen from: all 200 members, or only the members who swim.

Part (a)

1. Aged 30 or over and swim: 54.
2. Probability =\frac{54}{200}=\frac{27}{100}.

Part (b)

1. Members who swim: 36+54=90.
2. 36 of them are under 30.
3. Probability =\frac{36}{90}=\frac{2}{5}.

Check every pair of branches, and check the total number who said yes.

Part (a)

1. Men: 30+16=46, which is correct. First branches: 46+54=100, which is correct.
2. Yes: 30+25=55, which is correct.
3. Women: 25+32=57, but there are 54 women. So 32 is wrong.

Part (b)

1. Women who said no: 54-25=29.

Start with the customers who did not order a hot drink: how many of them did order cake?

Part (a)

1. No hot drink: 180-100=80.
2. 50 of these 80 customers did not order cake either.
3. No hot drink but cake: 80-50=30.

Part (b)

1. 72 customers ordered cake and 30 of them did not order a hot drink.
2. Hot drink and cake: 72-30=42.

Part (c)

1. 72 customers ordered cake and 42 of them also ordered a hot drink.
2. Probability =\frac{42}{72}=\frac{7}{12}.