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Either paper 3 marks
The bar chart shows the favourite ways to travel of some students.
(a)How many students chose Car?
(b)Calculate the difference between the most popular and the least popular.
(c)How many students were asked altogether?
Show answer
(a) \(30\)
(b) \(22\)
(c) \(88\)Read across from the top of the Car bar to the scale: 30.
The tallest bar is 30 and the shortest is 8.
\(30 - 8 = 22\)
Every person chose exactly one, so add the four bars:
\(8 + 26 + 30 + 24 = 88\)
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Either paper 3 marks51 people were asked to name their favourite pet. The table shows some of the results.
A bar chart is to be drawn from the table. Find the height of the Bird bar.Pet Frequency Dog 19 Cat 9 Fish 11 Bird Show answer
\(12\)The four frequencies add up to 51, and three of them are known:
\(19 + 9 + 11 = 39\)
So the Bird frequency is
\(51 - 39 = 12\)
and the Bird bar is drawn to a height of 12.
- M1adds the known frequencies \(19 + 9 + 11 = 39\)
- M1subtracts from the total \(51 - 39\)
- A1Bird bar height \(12\)
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Either paper 2 marks
On a journey, Amara sees 38 vehicles. Each vehicle is a car, a van or a motorbike.
Amara draws this bar chart.
Make two criticisms of her bar chart.
Show answer
Any two of: the horizontal axis has no label; the chart has no title; the bars do not add up to the number of vehicles seen.Check the chart's structure first: it has no title, and an axis with a blank name does not say what it shows.
Then add the three bars and compare with the number of vehicles Amara saw:
\(16 + 16 + 12 = 44\)
Amara saw \(38\) vehicles and the bars add up to \(44\). These are not equal, so the total is a criticism.
Any two of these are valid criticisms: the horizontal axis has no label; the chart has no title; the bars do not add up to the number of vehicles seen.
- B1one valid criticism from: the horizontal axis has no label; the chart has no title; the bars do not add up to the number of vehicles seen
- B1a second, different valid criticism from: the horizontal axis has no label; the chart has no title; the bars do not add up to the number of vehicles seen
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Either paper 5 marks
24 children were asked which pet they each like best. Here are the results.
Rabbit, Cat, Rabbit, Cat, Rabbit, Dog, Rabbit, Dog, Cat, Dog, Cat, Cat, Rabbit, Dog, Cat, Dog, Rabbit, Rabbit, Rabbit, Cat, Dog, Dog, Dog, Dog
(a) Complete the frequency table.Pet Tally Frequency Dog Cat Rabbit (b)Write down the mode.
(c)Draw a bar chart on the grid to show the results.
Use a vertical scale of 1 square for every 2 children.
You cannot draw on this page. Draw (c) on paper, then show the answer and check your drawing against the model.
Show answer
(a) \(9, 7, 8\) for Dog, Cat, Rabbit
(b) Dog
(c) Bars to 9, 7 and 8 in the order of the table, on a vertical axis numbered 2 to a square(c)Go through the list once, ticking each item off as it is counted.
Dog: 9, Cat: 7, Rabbit: 8
Check: \(9 + 7 + 8 = 24\), the number of children asked.
The mode is the most common choice, the one with the greatest frequency: Dog, with 9.
One square stands for 2, so halve each frequency.
Dog: \(9 \div 2 = 4.5\) squares
Cat: \(7 \div 2 = 3.5\) squares
Rabbit: \(8 \div 2 = 4\) squares
- (a) M1each item counted once, giving Dog 9, Cat 7, Rabbit 8, with at most one count wrong
- (a) A1all three frequencies correct, adding to 24
- (c) B1the vertical axis numbered 2 to a square
- (c) B1all three bars drawn to the right height: Dog 9, Cat 7 and Rabbit 8 (4.5, 3.5 and 4 squares)
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Either paper 2 marksSome people were asked to name their favourite pet. The table shows the results.
The bar chart shows two of the results. Complete the bar chart.Pet Frequency Dog 10 Cat 11 Fish 14 Bird 9 You cannot draw on this page. Draw this on paper, then show the answer and check your drawing against the model.
Show answer
The Cat bar drawn to \(11\) and the Bird bar drawn to \(9\)The bars for Cat and Bird are missing.
The frequency axis goes up in 2s, so a whole number that is not marked is half-way between two lines.
The table gives Cat a frequency of \(11\), so its bar stops at \(11\).
The table gives Bird a frequency of \(9\), so its bar stops at \(9\).
- B1one of the two missing bars drawn to the right height
- B1both missing bars drawn to the right height
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Either paper 3 marks
The bar chart shows information about a sports club.
(a)How many are shown for Seniors in Squash?
(b)Calculate the difference between Juniors and Seniors in Squash.
(c)Which group has the larger total across all three?
Show answer
(a) \(19\)
(b) \(7\)
(c) SeniorsFind Squash along the bottom, then the Seniors bar of the pair — the key says which is which. It reaches 19.
The two Squash bars are 12 and 19.
The difference is 7.
Juniors: \(14 + 12 + 23 = 49\)
Seniors: \(24 + 19 + 19 = 62\)
So Seniors has the larger total, by 13.
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Either paper 4 marks
The bar chart shows how the students in a class travel to school.
(a)Work out the total number of students.
(b)Work out the fraction of the students in the bar for Bus.
Give your answer in its simplest form.
Show answer
(a) \(44\ \text{students}\)
(b) \(\frac{3}{11}\)Add the four bars.
\(13 + 12 + 5 + 14 = 44\) students
The bar for Bus is \(12\) out of the \(44\) altogether.
\(\frac{ 12 }{ 44 } = \frac{3}{11}\)
- (a) M1adds the four bar heights \(13 + 12 + 5 + 14\)
- (a) A1total \(44\)
- (b) M1fraction \(\frac{ 12 }{ 44 }\)
- (b) A1simplified to \(\frac{3}{11}\)
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Either paper 4 marks
A survey asked people to name their favourite pizza topping.
The bar chart shows the results for three of the four answers, but the bar for Pepper has not been drawn.
\(51\) people took part altogether.
(a)Find the height of the bar for Pepper.
(b)Write down the most common answer.
(c)Another survey is carried out with twice as many people, and the results are in the same proportions.
Calculate how many would choose Pepper.
Show answer
(a) \(11\ \text{people}\)
(b) Mushroom
(c) \(22\ \text{people}\)Read the three drawn bars off the frequency axis and add them.
\(15 + 9 + 16 = 40\)
Everyone who took part is in one of the four bars, so what is left over belongs to Pepper.
\(51 - 40 = 11\) people
Compare all four frequencies, including the one just worked out: \(15\), \(9\), \(16\) and \(11\).
The largest is \(16\), so the most common answer is Mushroom.
Twice as many people in the same proportions means every bar doubles.
\(11 \times 2 = 22\) people
- (a) M1adds the three drawn bars \(15 + 9 + 16 = 40\)
- (a) A1subtracts from the total to get \(11\)
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Either paper 3 marks
Students choose a juice with their school meal. The numbers who choose Orange, Apple and Lime are in the ratio
\(Orange : Apple : Lime = 4 : 5 : 1\)
The bar chart has been drawn for one of the three choices only.
Complete the bar chart.
You cannot draw on this page. Draw this on paper, then show the answer and check your drawing against the model.
Show answer
The Orange bar drawn to \(8\) and the Lime bar drawn to \(2\)The Apple bar is drawn to a height of \(10\), and its share of the ratio is \(5\).
One part is worth
\(10 \div 5 = 2\)
The Orange share of the ratio is \(4\), so its bar is
\(4 \times 2 = 8\)
The Lime share of the ratio is \(1\), so its bar is
\(1 \times 2 = 2\)
- M1one part worked out as \(10 \div 5 = 2\), shown by a missing bar drawn to the right height
- A1one of the two missing bars drawn to the right height
- A1the Orange bar drawn to \(8\) and the Lime bar drawn to \(2\)
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Either paper 4 marks
\(57\) people each choose one of Bear, Rhino, Ox or Lion as their team mascot.
The bar chart shows the number of people who chose two of these.
The number of people who chose Bear is \(2\) more than the number of people who chose Lion.
Complete the bar chart.
You cannot draw on this page. Draw this on paper, then show the answer and check your drawing against the model.
Show answer
The Bear bar drawn to \(10\) and the Lion bar drawn to \(8\)The two bars that are drawn show \(19\) and \(20\) people.
\(19 + 20 = 39\)
The other two bars share what is left of the \(57\) people.
\(57 - 39 = 18\)
Bear is \(2\) more than Lion. Take the \(2\) away and the two bars are equal.
\(18 - 2 = 16\)
Share that equally between the two bars.
\(16 \div 2 = 8\)
So the Lion bar stops at \(8\), and the Bear bar is \(2\) higher.
\(8 + 2 = 10\)
Check: \(19 + 20 + 10 + 8 = 57\).
- M1adds the two drawn bars, \(19 + 20 = 39\)
- M1subtracts from the total to get \(18\) for the two missing bars
- M1removes the difference and halves, so at least one missing bar is drawn to its right height
- A1both missing bars drawn to the right height, Bear \(10\) and Lion \(8\)