Displaying and interpreting data booklet
Displaying and interpreting data booklet
- Unit 1: Numbers
- Unit 2: Geometry and measure
- Unit 3 : Statistics and probability
In this topic you will
- Record, organise, and represent data using diagrams and charts.
- Interpret and compare data to answer statistical questions.
Key Words
- bar chart
- Carroll diagram
- pictogram
- Venn diagram
Show Definitions
- bar chart: A chart that uses rectangular bars to show and compare numerical data across categories.
- Carroll diagram: A table used to sort items into groups based on two different criteria.
- pictogram: A diagram that uses pictures or symbols to represent data, where each symbol stands for a fixed number.
- Venn diagram: A diagram made of overlapping circles that shows relationships and similarities between sets.
Displaying and Comparing Data
I n this unit, you will explore different ways of displaying data so that it is easier to understand and interpret. You will use Carroll diagrams and Venn diagrams to sort data, and bar charts and pictograms to compare different sets of data.
Worked example $1$
Put these shapes into the Venn diagram.
Answer
❓ EXERCISES
$1$. Look at the children.
Copy the Venn diagram and sort each child into the correct section.
👀 Show answer
Curly hair only: Sophie
Glasses only: Yutu, Petra, Adith
Earrings only: Antonella
Curly hair and glasses: Filip, Norman
No circles (not curly hair, not glasses, not earrings): Sun, Tapu
Note: Place each child by matching what you can see (curly hair, glasses, earrings).
$2$. Copy the Venn diagram and fill in the numbers $1$ to $30$.
👀 Show answer
Multiples of $2$ only: $2, 4, 8, 14, 16, 22, 26, 28$
Multiples of $3$ only: $3, 9, 21, 27$
Multiples of $5$ only: $5, 25$
Multiples of $2$ and $3$ (not $5$): $6, 12, 18, 24$
Multiples of $2$ and $5$ (not $3$): $10, 20$
Multiples of $3$ and $5$ (not $2$): $15$
Multiples of $2$, $3$ and $5$: $30$
Outside all circles: $1, 7, 11, 13, 17, 19, 23, 29$
$3$.
a. Copy and complete the Carroll diagram.
Put the numbers $1$ to $20$ into the Carroll diagram.
b. Copy and complete this sentence to explain why one of the sections of the Carroll diagram does not contain any numbers.
There cannot be any number in the section ______ because ______.
👀 Show answer
a.
Multiple of $10$ and even: $10, 20$
Multiple of $10$ and not even: (none)
Not a multiple of $10$ and even: $2, 4, 6, 8, 12, 14, 16, 18$
Not a multiple of $10$ and not even: $1, 3, 5, 7, 9, 11, 13, 15, 17, 19$
b. There cannot be any number in the section multiple of $10$ and not even because every multiple of $10$ ends in $0$, so it is always even.
$4$. Class $4$ watched the road outside their window.
They recorded the number of vehicles that passed between $9.00$ a.m. and $9.15$ a.m. and also the number of vehicles that passed between $2.00$ p.m. and $2.15$ p.m.
These two pictograms show the results.
a. How many cars passed the school between $9.00$ a.m. and $9.15$ a.m.?
b. How many buses passed the school between $2.00$ p.m. and $2.15$ p.m.?
c. During which time did most vans pass the school?
d. How many more motorcycles passed the school between $9.00$ a.m. and $9.15$ a.m. than between $2.00$ p.m. and $2.15$ p.m.?
e. How many vehicles passed the school in total between $9.00$ a.m. and $9.15$ a.m.?
f. During which time was the road outside the school busiest?
Explain how you know.
👀 Show answer
a. $24$
b. $1$
c. Between $2.00$ p.m. and $2.15$ p.m.
d. $3$
e. $46$
f. Between $9.00$ a.m. and $9.15$ a.m., because the total number of vehicles then is $46$, which is more than $42$ between $2.00$ p.m. and $2.15$ p.m.
$5$. Thirty children voted for their favourite singer.
Thirty adults also voted for their favourite singer.
a. Which singer received $13$ votes from the adults?
b. How many children voted for singer $2$?
c. How many more children than adults voted for singer $3$?
d. How many people in total voted for singer $4$?
e. Copy the sentence and complete it by writing something that is similar about the data in the two graphs.
Both the adults and children ____.
f. Conjecture about the differences in the data between the two graphs.
Copy and complete the sentence by writing what is different about the data in the two graphs.
The children _____, but the adults ____.
g. Copy and complete the sentence to give a possible reason why the data in the graphs is different.
I think that the data for the children’s vote and the data for the adults’ vote is different because ____.
👀 Show answer
a. Singer $1$
b. $0$
c. $3$
d. $26$
e. Both the adults and children voted for singer $1$.
f. The children gave the most votes to singer $4$, but the adults gave the most votes to singer $1$.
g. I think that the data for the children’s vote and the data for the adults’ vote is different because children and adults often like different types of music and different singers.
$6$. Ahmed used a tally chart to collect data about the number of people in households.
| Number of people living in a household | Tally | Frequency |
|---|---|---|
| $1$ to $3$ | ||||| | $5$ |
| $4$ to $6$ | ||||| ||||| ||||| || | $17$ |
| $7$ to $9$ | ||||| ||| | $8$ |
a. How many households had between $7$ to $9$ people?
b. Ahmed says that his data shows that $17$ households had $4$ people in them.
Is he correct? Explain your answer.
Draw a tally chart and collect data from people in your classroom about the number of people in their households.
Write two sentences describing what is different and what is similar between the data in your table and the data in the table above.
👀 Show answer
a. $8$
b. No. The $17$ is the number of households with between $4$ and $6$ people, not exactly $4$ people.
Example for the last two tasks: Your own tally chart and comparison will depend on your classroom data.
Example comparison sentences: “Both sets of data have the most households in the $4$ to $6$ range. My class data has fewer households in the $7$ to $9$ range than Ahmed’s data.”
$7$. Three students used a table to record the scores in a test.
| Learner | Score |
|---|---|
| Moira | $138$ |
| Olivia | $121$ |
| Parveen | $154$ |
The three graphs show this information.
Which one shows the results best?
Explain your answer.
👀 Show answer
Graph $2$ shows the results best because it uses a sensible scale that fits the scores closely, so the differences between $121$, $138$, and $154$ are easy to see.
$8$. Class $1$ and Class $2$ took a Maths test. These frequency tables show how many children got each score on the test.
| Class $1$ | Class $2$ | |||
|---|---|---|---|---|
| Score | Number of children | Score | Number of children | |
| $0$ | $2$ | $0$ | $0$ | |
| $1$ | $3$ | $1$ | $2$ | |
| $2$ | $2$ | $2$ | $2$ | |
| $3$ | $4$ | $3$ | $6$ | |
| $4$ | $11$ | $4$ | $9$ | |
| $5$ | $8$ | $5$ | $11$ | |
a. Would a Carroll diagram or a pictogram be better for displaying this data?
b. A bar chart would also be a good way to represent the data.
Draw two bar charts to display the data.
You will need to:
• choose a scale
• label the horizontal axis and the vertical axis.
• add a title
c. Describe one way that the data in the graphs is similar.
d. Describe one way that the data in the graphs is different.
e. Why do you think that more children in Class $2$ had higher scores?
👀 Show answer
a. A pictogram would be better, because the data is a single category (score) with frequencies, and a Carroll diagram is mainly used for sorting by two criteria.
b. Your two bar charts should have scores $0$ to $5$ on the horizontal axis and number of children on the vertical axis, with a clear scale and titles for Class $1$ and Class $2$.
c. In both classes, most children scored $4$ or $5$ (the higher scores).
d. Class $2$ has more children scoring $5$ ($11$) than Class $1$ ($8$), and Class $2$ has no children scoring $0$.
e. For example, Class $2$ may have had more practice, different teaching, or found the test easier.
🧠 Think like a Mathematician
Create a poster showing the different ways of displaying data and when they can be used. Show the different characteristics of each and critique their advantages and disadvantages. Include:
- Venn diagram
- Carroll diagram
- tally chart
- frequency table
- dot plot
- pictogram
- bar chart.
Suggested structure for your poster:
- Write the name of each display and draw a small example of it.
- Explain what kind of data it is best for (e.g., categories, frequencies, sorting).
- List at least $2$ advantages and $2$ disadvantages for each one.
- Finish with a short comparison: which display is best for sorting, and which is best for comparing amounts?
👀 show answer
- Venn diagram: Best for showing overlaps between sets. Advantage: shows shared properties clearly. Disadvantage: gets messy with many sets.
- Carroll diagram: Best for sorting using $2$ criteria. Advantage: very clear “yes/no” sorting. Disadvantage: limited to two properties at a time.
- Tally chart: Best for collecting data quickly. Advantage: fast and simple during counting. Disadvantage: you usually need to convert tallies into totals to compare easily.
- Frequency table: Best for summarising counts for each category/value. Advantage: organised and easy to total. Disadvantage: patterns can be harder to “see” than in a graph.
- Dot plot: Best for small sets of numerical data. Advantage: shows clusters, gaps, and repeats clearly. Disadvantage: not good for very large data sets.
- Pictogram: Best for simple comparisons using pictures/symbols. Advantage: easy to read and engaging. Disadvantage: can be inaccurate if symbols represent fractions or if the key is unclear.
- Bar chart: Best for comparing amounts across categories. Advantage: differences are easy to spot. Disadvantage: misleading if the scale is uneven or does not start at $0$.