Bar Charts and Composite Bar Charts

Worked example

1. 1

   $\text{1 square}=2$ — Read the scale first. The labels up the side go 0, 2, 4, 6 …, so each square is worth 2 emails, not 1.

2. 2

   $\text{Wed}=15$ — “Which day had the most?” Find the tallest bar. Wednesday's bar stops at 15. The group with the most is called the mode.

3. 3

   $\text{Tue: halfway from }6\text{ to }8$ — Tuesday's bar stops in the middle of a square, between the 6 line and the 8 line.

4. 4

   $\text{Tue}=7$ — Half a square is half of 2, which is 1. So the bar shows 6 + 1 = 7.

5. 5

   $\text{Mon}=12=2\times 6$ — “Which day had twice as many as Thursday?” Thursday is 6, and 2 × 6 = 12. The bar at 12 is Monday.

Worked example

1. 1

   $12+7+15+6+9$ — “How many emails altogether?” Read every bar, Monday to Friday, and write them as a sum.

2. 2

   $=49\text{ emails}$ — Add one at a time: 12 + 7 = 19, 19 + 15 = 34, 34 + 6 = 40, 40 + 9 = 49.

3. 3

   $\text{Wed}-\text{Thu}=15-6$ — “How many more on Wednesday than Thursday?” More means take the smaller bar from the bigger one.

4. 4

   $=9\text{ emails}$ — 15 − 6 = 9. Check: 6 + 9 = 15, so Wednesday had 9 more.

Worked example

1. 1

   $4\text{ squares}=12\text{ games}$ — The draw bar is the one we know: 4 squares tall, and the question says 12 games.

2. 2

   $1\text{ square}=12÷4=3$ — Divide to find what one square is worth: 3 games.

3. 3

   $\text{won}=6\times 3=18$ — Now read any bar. The won bar is 6 squares, so 18 games were won.

4. 4

   $18\times 3+12\times 1=66$ — Turn games into points: 18 wins × 3 = 54, 12 draws × 1 = 12, and 54 + 12 = 66 points. Losses score 0.

Worked example

1. 1

   $18+12+21+9=60$ — Find the total first by adding every bar. If the question already gives the total, use that.

2. 2

   $\text{banana}=12$ — “What fraction chose banana?” Read the bar for that group only.

3. 3

   $\frac{12}{60}$ — Put the bar over the total.

4. 4

   $=\frac{1}{5}$ — Simplify: 12 and 60 both divide by 12. One fifth of the students chose banana.

Worked example

1. 1

   $18+21=39$ — “What percentage chose apple or mango?” Add the two bars asked about first.

2. 2

   $\frac{39}{60}\times 100$ — Bar over total, then × 100 turns the fraction into a percentage.

3. 3

   $=65\%$ — 39 ÷ 60 = 0.65, and 0.65 × 100 = 65. Check: 65% of 60 is 39.

Worked example

1. 1

   $14+18+11+20=63$ — Read the four bars you can see and add them: 63 cakes.

2. 2

   $75-63=12$ — The total is 75, so what is left, 12, must be Friday.

3. 3

   $\text{Friday bar up to }12$ — Draw it the same width as the others, with a gap, stopping at 12 on the scale.

4. 4

   $14+18+11+20+12=75$ — Check: all five bars now add up to the total.

Steps

1. 1

   Label the side "Frequency" and write a label under each bar.

2. 2

   Pick a scale that fits the biggest value, 14. Going up in 2s works.

3. 3

   Draw every bar the same width, with equal gaps.

4. 4

   Draw each bar up to its value: Juice stops halfway between 4 and 6.

Worked example

1. 1

   $\text{Sat}=2\times \text{Tue}$ — One missing bar, given in words: Saturday was twice Tuesday. So read Tuesday from the chart first.

2. 2

   $=2\times 7$ — Tuesday's bar shows 7 emails.

3. 3

   $=14$ — 2 × 7 = 14. Draw Saturday's bar up to 14, the same width as the others, with a gap.

Worked example

1. 1

   $0,2,4,6,10,15$ — Look at the steps on the scale: 2, 2, 2, then 4, then 5. Equal spaces must mean equal steps, so the scale is wrong.

2. 2

   $\text{dog bar}=\text{wider}$ — Compare the widths. Every bar must be the same width, because a wider bar looks like more than it is.

3. 3

   $\text{side axis: no label}$ — Each axis needs a label, like “Frequency”, so the reader knows what the numbers count.

4. 4

   $\text{2 reasons}=\text{2 marks}$ — Write each reason as a sentence, e.g. “The scale does not go up in equal steps.” Each different reason earns 1 mark.

Worked example

1. 1

   $\text{key: }\text{Tom},\text{Ali}$ — Read the key first, so you know which bar belongs to whom.

2. 2

   $\text{Wed: }12=2\times 6$ — “On which day did Ali send twice as many as Tom?” On Wednesday Ali's bar is 12 and Tom's is 6, and 2 × 6 = 12.

3. 3

   $\text{Thu: }9=9$ — “When did they send the same?” Look for two bars of equal height: Thursday, 9 each.

4. 4

   $12+7+12+9=40$ — “How many did Ali send in total?” Add only Ali's bars, Monday to Thursday: 40 texts.

Worked example

1. 1

   $\text{cycling}=6-0=6$ — The bottom part starts at 0, so its top on the scale is its value: 6 hours.

2. 2

   $\text{swimming}=10-6=4$ — The middle part starts at 6, not 0. Take where it starts from where it ends: 4 hours.

3. 3

   $\text{running}=15-10=5$ — The top part runs from 10 to 15, so 5 hours.

4. 4

   $6+4+5=15$ — Check: the three parts add up to the height of the whole bar.