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Charts
The results of measurements are often displayed on charts instead of tables.
Obtaining data from charts
Example 1
Study the bar chart showing the number of subscribers of a maths journal for kids (rounded to the nearest hundred) each \latex{ year }.
\latex{ subscribers }
\latex{ year }
\latex{ 1,000 }
\latex{ 4,000 }
\latex{ 3,000 }
\latex{ 2,000 }
\latex{ 2024 }
\latex{ 2019 }
\latex{ 2020 }
\latex{ 2021 }
\latex{ 2022 }
\latex{ 2023 }
Solution
The height of the bars shows the number of subscribers.
number of
subscribers
\latex{year}
\latex{ 2019 }
\latex{ 1,000 }
\latex{ 1,300 }
\latex{ 1,900 }
\latex{ 2,600 }
\latex{ 3,400 }
\latex{ 4,000 }
\latex{ 2024 }
\latex{ 2023 }
\latex{ 2022 }
\latex{ 2021 }
\latex{ 2020 }
The increase in the number of subscribers is clearly visible on the bar chart.
Example 2
In a TV show, contestants must choose the correct answer out of four options. The contestants can ask \latex{ 100 } people in the audience for help.
Question: What is a dingo?
The possible answers:
\latex{ A }: a game; \latex{ B }: liquorice; \latex{ C }: wild dog; \latex{ D }: a horse-drawn sleigh.
\latex{ A }: a game; \latex{ B }: liquorice; \latex{ C }: wild dog; \latex{ D }: a horse-drawn sleigh.
Study the bar chart to determine which option received the most votes from the audience.
person
\latex{ D }
\latex{ 100 }
\latex{ 90 }
\latex{ 80 }
\latex{ 70 }
\latex{ 60 }
\latex{ 50 }
\latex{ 40 }
\latex{ 30 }
\latex{ 20 }
\latex{ 10 }
\latex{ A }
\latex{ B }
\latex{ C }
Solution
\latex{ 79 } people voted for \latex{ C }, the wild dog. The occurrence of option \latex{ C } is \latex{ 79 }, that of option \latex{ A } is \latex{ 11 }, that of option \latex{ B } is \latex{ 9 }, and that of option \latex{ D } is \latex{ 1 }.
The occurrence of a value is the number of times it appears in the data set.
Example 3
The chart shows the average rainfall in Balzan each \latex{ month } over the past \latex{ 100 } \latex{ years }.
Use the chart to answer the following questions.
Sep.
Jan.
Mar.
May
\latex{mm }
Jul.
Nov.
\latex{ 0 }
\latex{ 5 }
\latex{10 }
\latex{15 }
\latex{20 }
\latex{25 }
- Which are the most and least rainy months?
- In which successive months does the amount of rainfall increase, and in which ones does it decrease?
- Which are the two successive months with the largest difference in rainfall?
Solution
- July was the driest month, whereas the most rain fell in December.
- Rainfall increases from August to December. It decreases from January to July.
- August and September are the two successive months where the difference in rainfall is the largest; that is, the difference between two neighbouring bars is the largest here.
Displaying data on charts
Example 4
Use charts to summarise the information about the following class (number of boys and girls, languages).
Mia
\latex{13} years
Spanish,
car,
swimming
car,
swimming
Alex
\latex{13} years
Spanish,
walking,
soccer
walking,
soccer
Olivia
\latex{14} years
French,
bike,
tennis
bike,
tennis
Sofia
\latex{13} years
German,
bus,
swimming
bus,
swimming
Ben
\latex{14} years
Spanish,
bike,
swimming
bike,
swimming
Carrie
\latex{13} years
German,
walking,
gymnastic
walking,
gymnastic
Jessica
\latex{13} years
German,
bus,
basketball
bus,
basketball
Richard
\latex{13} years
Spanish,
car,
swimming
car,
swimming
Stanford
\latex{14} years
Spanish,
car,
basketball
car,
basketball
Emil
\latex{13} years
French,
bike,
swimming
bike,
swimming
Steve
\latex{14} years
Spanish,
car,
basketball
car,
basketball
Jacob
\latex{13} years
German,
car,
handball
car,
handball
Anthony
\latex{13} years
French,
bus,
basketball
bus,
basketball
Lily
\latex{13} years
Spanish,
car,
swimming
car,
swimming
Harry
\latex{14} years
Spanish,
bus,
football
bus,
football
Thomas
\latex{14} years
Spanish,
bus,
handball
bus,
handball
Emily
\latex{13} years
French,
car,
gymnastic
car,
gymnastic
Jerry
\latex{14} years
German,
bike,
tennis
bike,
tennis
Miranda
\latex{13} years
Spanish,
bus,
basketball
bus,
basketball
Abigail
\latex{14} years
French,
bus,
swimming
bus,
swimming
Solution
Number of boys and girls:
\latex{ 11 }
boy
girl
\latex{ 9 }
girls
No.
\latex{ 10 }
\latex{ 5 }
boys
You can see that there are almost the same number of girls and boys.
Languages:
Languages:
\latex{ 10 }
Spanish
German
French
\latex{ 5 }
\latex{ 5 }
French
No.
\latex{ 10 }
\latex{ 5 }
Spanish
German
You can see that half of the students study Spanish, a quarter of them study French and a quarter of them German. This information can be represented using a pie chart. The proportion of the languages can be better illustrated on a pie chart than on a bar chart.
You can make the following table and chart to display how many boys and girls study each language.
French
Spanish
German
French
girl
boy
Spanish
German
No.
\latex{ 5 }
\latex{ 10 }
Spanish
German
French
You can see that twice as many boys learn Spanish. However, more girls study French and German.
Exercises
{{exercise_number}}. Collect more information about the class in Example 4 and display the data on a chart. Represent the data of boys and girls separately. Collect and illustrate similar data for your class.
{{exercise_number}}. Flip a coin \latex{ 20 } times, and record the frequency of heads and tails. Represent the result on a bar chart.
{{exercise_number}}. The bar chart shows the number of sandwiches sold in the school cafeteria in the first week of October.
Ask questions and answer them as well. (→)
\latex{ 20 }
No.
\latex{ 100 }
\latex{ 80 }
\latex{ 60 }
\latex{ 40 }
Friday
Monday
Tuesday
Wednesday
Thursday
{{exercise_number}}. The following charts show the average rainfall in Rome and in Colombo each month. Ask questions based on the charts and answer them.
Rome
Jan.
Mar.
May
Jul.
Sep.
Nov.
mm
\latex{ 300 }
\latex{ 250 }
\latex{ 200 }
\latex{ 150 }
\latex{ 100 }
\latex{ 50 }
\latex{ 0 }
Colombo
Jan.
Mar.
May
Jul.
Sep.
Nov.
mm
\latex{ 300 }
\latex{ 250 }
\latex{ 200 }
\latex{ 150 }
\latex{ 100 }
\latex{ 50 }
\latex{ 0 }
{{exercise_number}}. Roll a dice \latex{ 100 } times, and note the occurrences of each number. Represent the results on a bar chart.
{{exercise_number}}. Which of the following bar charts corresponds to the pie chart?
a)
\latex{ 1. }
\latex{ 2. }
\latex{ 3. }
\latex{ 4. }
\latex{ 5. }
b)
\latex{ 1. }
\latex{ 2. }
\latex{ 3. }
\latex{ 4. }
\latex{ 5. }
c)
\latex{ 1. }
\latex{ 2. }
\latex{ 3. }
\latex{ 4. }
\latex{ 5. }
{{exercise_number}}. Draw bar charts for the pie charts in the image below.
a)
b)
c)
d)
{{exercise_number}}. Represent the height of the following mountain peaks, rounded to the nearest thousand on a bar chart: Mount Everest \latex{ 8,848 } \latex{ m }; Mont Blanc \latex{ 4,807 } \latex{ m }; Etna \latex{ 3,340 } \latex{ m }; Gerlach \latex{ 2,655 } \latex{ m }; Kilimanjaro \latex{ 5,892 } \latex{ m }; Kékestető \latex{ 1,014 } \latex{ m }.
{{exercise_number}}. Use a pie chart to show that half of the students in a class have brown eyes, a quarter have blue eyes, and the rest have grey eyes. What is the ratio of students with grey eyes?
Quiz
A TV channel used a chart to show that the viewers of one of its cartoons increased multiple times. Is this statement true?
No. (thousand people)
Jan.
\latex{ 700 }
\latex{ 600 }
\latex{ 500 }
Sept.
Okt.
Nov.
Dec.
