Complete the tally chart for this data
1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 3
1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 3
Worked Solution & Answer
5, 2, 4 B1
Answer: Frequencies: 1 → 5, 2 → 2, 3 → 4
Bar charts — Notes & Worked Examples Show / Hide
Explanation:
Every bar chart for discrete data must have: (1) equal width bars, (2) equal gaps between bars, (3) a vertical frequency axis starting at 0 with a uniform scale, and (4) clear labels on both axes.
In a dual (comparative) bar chart, two bars are drawn side-by-side for each category with a key. In a composite (stacked) bar chart, sub-categories are stacked on top of each other, so subtract the bottom reading from the top reading to find the upper section’s frequency.
Example 1: The bar chart shows pupils’ favourite sports: Football = 12, Tennis = 7, Rugby = 5, Swimming = 10. Find (a) total pupils & (b) how many more chose Football than Tennis.
(a) Total: 12 + 7 + 5 + 10 = 34 pupils
(b) Difference: 12 − 7 = 5 more pupils
Example 2: The dual bar chart shows club attendance (Drama: 6B, 9G; Music: 8B, 7G; Coding: 11B, 5G). Find total girls & greatest difference.
• Total girls: 9 + 7 + 5 = 21 girls
• Greatest difference: Coding (11 − 5 = 6, vs Drama 3, Music 1)
Work out
5 people chose Green.
Complete the bar chart
5 people chose Green.
Complete the bar chart
Worked Solution & Answer
Height = 5 B1
Answer: Green bar drawn to height 5
A village has four bus stops.
The bar chart shows information about the people at the bus stops at 3 pm one day.
The bar chart shows information about the people at the bus stops at 3 pm one day.
(a) Two people were at the Football ground bus stop.
Show this information on the bar chart. [1 mark]
Show this information on the bar chart. [1 mark]
(b) How many more people were at the School bus stop than at the Post office bus stop? [1 mark]
Answer
Worked Solution & Answer
(a)
Draw a bar of height 2 at the Football ground position. B1
Answer (a): Bar of height 2 drawn for Football ground
(b)
School = 13, Post office = 4
13 - 4 = 9 B1
13 - 4 = 9 B1
Answer (b): Answer 9
The table shows information about the number of students who arrived late at school each day one week.
On the grid, draw a bar chart for this information.
Worked Solution & Answer
Equal-width bars drawn at 9, 10, 8, 6, 3 M2 A1
Answer: Bars of heights 9, 10, 8, 6, 3 drawn with linear scale and day labels
The bar chart shows information about the weight, in millions of tonnes, of bananas produced by each of four countries in 2016
(a) Draw a bar on the bar chart to show this information. [1 mark]
(b) Which country? [1 mark]
(c) What fraction of the 113 million tonnes of bananas was produced in India in 2016? [2 marks]
Worked Solution & Answer
(a)
Bar of height 13 drawn for China B1
Answer (a): Bar drawn for China at height 13
(b)
Brazil is at 6.8 B1
Answer (b): Brazil
(c)
India = 29 million → 29/113 M1 A1
Answer (c): 29113
The bar chart gives information about the volume of fresh water made per day from sea water in each of four countries in 2015
(a) Write down the volume of fresh water made per day from sea water in Saudi Arabia in 2015 [1 mark]
million m³
(b) How much more? [2 marks]
million m³
(c) Draw a bar on the bar chart to show this information. [1 mark]
Worked Solution & Answer
(a)
9.2
Answer (a): 9.2 million m³
(b)
8.4 − 3.8 = 4.6 M1 A1
Answer (b): 4.6 million m³
(c)
Bar for Qatar at height 1.7
Answer (c): Bar for Qatar at height 1.7
There are only 10p coins, 20p coins, 50p coins and £1 coins in a bag.
The bar chart shows information about the number of 10p coins and the number of 20p coins in the bag.
The bar chart shows information about the number of 10p coins and the number of 20p coins in the bag.
There are eight 50p coins in the bag.
There are three £1 coins in the bag.
There are three £1 coins in the bag.
(a) Use this information to complete the bar chart. [2 marks]
(b) Show that the total amount of money in the bag is less than £10 [3 marks]
Worked Solution & Answer
(a)
Completed bar chart (50p at 8, £1 at 3) M1 A1
Answer (a): Completed bar chart (50p at 8, £1 at 3)
(b)
12 × 10p = £1.20 M1
7 × 20p = £1.40
8 × 50p = £4.00 M1
3 × £1 = £3.00
Total = 1.20 + 1.40 + 4.00 + 3.00 = £9.60. £9.60 < £10 C1
7 × 20p = £1.40
8 × 50p = £4.00 M1
3 × £1 = £3.00
Total = 1.20 + 1.40 + 4.00 + 3.00 = £9.60. £9.60 < £10 C1
Answer (b): Shown (£9.60 < £10)
Shamira uses a tally chart to record the vehicles passing her school.
Here is her chart with the tallies.
Each 5-bar gate represents 5 vehicles.
@@TABULAR0@@
Here is her chart with the tallies.
Each 5-bar gate represents 5 vehicles.
@@TABULAR0@@
(a) Shamira says,
“The number of cars is more than the total of the other vehicles because cars have four 5-bar gates and the others only have three 5-bar gates.”
Is she correct?
Tick a box.
[ ] Yes [ ] No
Show working to support your answer. [2 marks]
“The number of cars is more than the total of the other vehicles because cars have four 5-bar gates and the others only have three 5-bar gates.”
Is she correct?
Tick a box.
[ ] Yes [ ] No
Show working to support your answer. [2 marks]
(b) On the grid, draw a bar chart to represent the data in the tally chart. [3 marks]
Worked Solution & Answer
(a)
Total of other vehicles = 12 + 9 + 4 = 25 M1
Number of cars = 23
Since 23 < 25, cars are not more than the total of other vehicles
So she is incorrect (No). A1
Number of cars = 23
Since 23 < 25, cars are not more than the total of other vehicles
So she is incorrect (No). A1
Answer (a): No
(b)
Draw vertical bars of equal width with correct frequencies: M2
Car = 23, Bus = 12, Van = 9, Lorry = 4. A1
Car = 23, Bus = 12, Van = 9, Lorry = 4. A1
Answer (b): Bar chart with bars of height 23 (Car), 12 (Bus), 9 (Van), 4 (Lorry)
A teacher asks the students in Year 6 what type of transport they use to get to school.
The dual bar chart shows some of the results.
The dual bar chart shows some of the results.
(a) What is the most popular type of transport used by the boys? [1 mark]
(b) Show this information on the dual bar chart. [1 mark]
(c) How many more? [1 mark]
(d) What is the total number of students in Years 5 and 6? [2 marks]
Worked Solution & Answer
(a)
Walk (9 boys) B1
Answer (a): Walk
(b)
Bar up to 7 B1
Answer (b): Bar of height 7 drawn for girls in Walk
(c)
Car = 5 + 9 = 14, Bus = 6 + 4 = 10 → 14 – 10 = 4 B1
Answer (c): 4
(d)
Year 6 = 14 + 10 + 16 + 5 + 3 = 48 M1
Years 5 & 6 = 48 × 2 = 96 A1
Years 5 & 6 = 48 × 2 = 96 A1
Answer (d): 96
The composite bar chart shows the number of students in some classes.
(a) How many boys are in the Physics class? [1 mark]
Answer
(b) How many girls are in the English class? [1 mark]
Answer
(c) Which two classes have the same total number of students? [1 mark]
Answer
(d) In the History class
there are 18 students
number of boys = number of girls
Show this information on the bar chart. [2 marks]
there are 18 students
number of boys = number of girls
Show this information on the bar chart. [2 marks]
Worked Solution & Answer
(a)
Looking at the Physics bar, the shaded boys section goes from 0 up to 8. B1
Answer (a): Answer 8
(b)
In the English bar, the total height is 29 and the boys section is 13
Number of girls = 29 - 13 = 16. B1
Number of girls = 29 - 13 = 16. B1
Answer (b): Answer 16
(c)
Total in Physics = 23
Total in French = 23
Both classes have 23 students. B1
Total in French = 23
Both classes have 23 students. B1
Answer (c): Answer Physics and French
(d)
Number of boys = 18 ÷ 2 = 9 M1
Number of girls = 9
Draw a bar for History with boys section up to 9 and total height up to 18. A1
Number of girls = 9
Draw a bar for History with boys section up to 9 and total height up to 18. A1
Answer (d): History bar drawn with total height 18, shaded boys section from 0 to 9, and unshaded girls section from 9 to 18.