Representing and interpreting data
🎯 In this topic you will
- Investigate statistical questions by collecting data
- Represent data using tables, bar charts, dot plots, and waffle diagrams
- Identify patterns in data to answer statistical questions
🧠 Key Words
- bar chart
- data
- dot plot
- statistical question
- waffle diagram
Show Definitions
- bar chart: A graph that uses rectangular bars to show and compare the sizes or frequencies of different categories.
- data: Information collected through observation, measurement, or inquiry that can be analyzed to answer questions.
- dot plot: A simple graph that displays each data value as a dot above a number line, showing frequency clearly.
- statistical question: A question that expects answers with variability and can be explored using data.
- waffle diagram: A grid-based chart where each small square represents part of a whole, often used to show proportions.
Exploring Ways to Show Data
I n this section you will explore and use different ways to display data so you can understand and interpret it more easily. You will use bar charts, dot plots and waffle diagrams to help you compare different sets of data.
💡 Quick Math Tip
Use a grid to represent totals accurately: When creating a waffle diagram, choose a rectangular grid with exactly one square for each data point. For example, if the total is 20, any grid that contains 20 squares (such as 5×4) will work and keeps proportions easy to colour and compare.
❓ EXERCISES
$1.$ This dot plot shows the ages of children visiting a zoo.
a. How many $2$ year old children were at the zoo?
b. How many children over $9$ years old were at the zoo?
c. The zoo wants to create a new play area for children at the zoo. What ages should the play area be aimed at? Explain using the dot plot.
👀 Show answer
a. $13$ children.
b. $2$ children.
c. Ages $2$–$8$ have the highest frequencies, so the play area should target this range.
$2.$ Jug A contains $2$ litres of water. Jug B contains $1$ litre. The amounts change during the day.
The graphs use different scales. Draw Jug B again using the same scale as Jug A.
a. How much water was in Jug A at $40$ minutes?
b. How much water was in Jug B at $40$ minutes?
c. How many times was each jug refilled?
d. How much more water was in Jug A than Jug B at $60$ minutes?
e. How much water was in the jugs altogether at $20$ minutes?
f. When were they closest to having no water?
👀 Show answer
a. $0.6$ L
b. $0.4$ L
c. Each jug refilled $2$ times.
d. Difference = $1.2$ L
e. Total ≈ $1.7$ L
f. Around $40$ minutes.
$3.$ This waffle diagram shows the number of books $30$ people read in a month.
a. How many read $0$ books?
b. How many read more than $4$ books?
c. What fraction read $2$ books?
d. What percentage read $3$ books?
👀 Show answer
a. $1$ person.
b. $0$ people.
c. $\frac{10}{30} = \frac{1}{3}$
d. $50\%$
$4.$ This waffle diagram shows the percentages of flavours sold by an ice cream company in one month.
a. Copy and complete the frequency table.
b. What percentage were not chocolate?
👀 Show answer
a. Strawberry: $25\%$ Vanilla: $5\%$ Mint: $20\%$ Chocolate: $49\%$ Blackcurrant: $1\%$
b. $51\%$ were not chocolate.
$5.$ These tally charts show visitor numbers for two hotels.
a. Complete the Snowy Mountain tally chart.
b. Draw a bar chart for Hotel Beachfront.
c. Describe the pattern.
d. Draw a dot plot for Snowy Mountain.
e. Describe the pattern.
f. Give one explanation for the differences.
👀 Show answer
a. Completed visitor numbers: Jan $30$, Feb $28$, Mar $22$, Apr $13$, May $10$, Jun $8$, Jul $8$, Aug $8$, Sept $9$, Oct $10$, Nov $18$, Dec $28$.
b. Bars rise to a peak mid-year then fall.
c. Beachfront: rises to summer then drops.
d. One dot per month's visitor total.
e. Snowy Mountain dips mid-year then rises again.
f. Seasonal tourism differences (summer beach vs winter snow).
🧠 Think like a Mathematician
Work on this investigation independently.
Hamza is making bracelets for children. He puts a tile on the bracelet for each letter in the child’s name, so he needs to know how many letters there are in the names.
Task: Determine how many tiles Hamza should put on the bracelets.
Decide how you will collect data to answer this question. You will need to choose which children you will include and how many data points you will gather.
Record your data in a table like the one shown below.
| Tally | Frequency | |
|---|---|---|
After collecting your data, create one of the following to represent it:
- Dot plot
- Bar chart
- Waffle diagram
You are convincing when you use your collected data as evidence for your solution.