160r. Interpreting Data Displays

Learning Intentions

• Learn the meaning of the terms numerical, categorical, discrete and continuous
• Interpret column graphs, line graphs and pie charts
• Interpret data presented in a table

Pre-requisite Summary

• Data is information collected about people, objects or events
• A data display is a way of organising information so that it can be read and compared
• Categories group data by type or label rather than by number
• Numerical data uses numbers to describe an amount or measurement
• Discrete data takes separate countable values
• Continuous data can take any value within an interval, depending on the level of accuracy used
• Tables, graphs and charts each present the same idea in different ways
• To interpret a display, it is important to read titles, labels, scales, headings and units carefully

Worked Examples

Worked Example 1
State whether each type of data is numerical or categorical.
a) favourite sport
b) height of a student
c) number of pets

Worked Example 2
State whether each type of numerical data is discrete or continuous.
a) number of books read in a month
b) mass of a watermelon
c) number of goals scored

Worked Example 3
A column graph shows the number of students choosing each fruit: apples $8$, bananas $5$, oranges $6$, pears $3$.
Answer the following.
a) Which fruit was chosen by the most students?
b) How many students chose bananas?
c) How many more students chose apples than pears?

Worked Example 4
A line graph shows the temperature at midday over five days: Monday ${22}^{\circ }\text{C}$, Tuesday ${24}^{\circ }\text{C}$, Wednesday ${21}^{\circ }\text{C}$, Thursday ${25}^{\circ }\text{C}$, Friday ${23}^{\circ }\text{C}$.
Answer the following.
a) On which day was the temperature highest?
b) What was the temperature on Wednesday?
c) How much did the temperature increase from Wednesday to Thursday?

Worked Example 5
A pie chart shows how students travel to school: walking ${90}^{\circ }$, bus ${120}^{\circ }$, car ${60}^{\circ }$, bike ${90}^{\circ }$.
Answer the following.
a) Which travel method is most common?
b) Which two travel methods are equal in size?
c) What fraction of the circle represents travel by car?

Worked Example 6
A table shows the number of library books borrowed in one week.

Answer the following.
a) On which day were the most books borrowed?
b) How many books were borrowed on Wednesday?
c) How many books were borrowed altogether on Monday and Tuesday?

Problems

Problem 1
State whether each type of data is numerical or categorical.
a) eye colour
b) age of a person
c) number of siblings

Problem 2
State whether each type of numerical data is discrete or continuous.
a) number of cars in a car park
b) length of a pencil
c) number of text messages sent

Problem 3
A column graph shows the number of votes for four games: Soccer $10$, Tennis $4$, Basketball $7$, Hockey $5$.
Answer the following.
a) Which game received the most votes?
b) How many votes did Tennis receive?
c) How many more votes did Soccer receive than Hockey?

Problem 4
A line graph shows rainfall over five days: Monday $3$ mm, Tuesday $6$ mm, Wednesday $2$ mm, Thursday $8$ mm, Friday $5$ mm.
Answer the following.
a) On which day was rainfall highest?
b) What was the rainfall on Wednesday?
c) How much greater was Thursday's rainfall than Monday's?

Problem 5
A pie chart shows favourite pets: dog ${180}^{\circ }$, cat ${90}^{\circ }$, fish ${45}^{\circ }$, bird ${45}^{\circ }$.
Answer the following.
a) Which pet is most popular?
b) Which two pets are equal in size?
c) What fraction of the circle represents cats?

Problem 6
A table shows the number of sandwiches sold.

Answer the following.
a) On which day were the most sandwiches sold?
b) How many were sold on Tuesday?
c) How many were sold altogether on Thursday and Friday?

Exercises

Understanding and Fluency

1. Classify each type of data as numerical or categorical.
   a) hair colour
   b) temperature
   c) number of students in a class
   d) favourite movie

2. Classify each type of numerical data as discrete or continuous.
   a) number of goals scored
   b) height of a tree
   c) number of marbles in a jar
   d) time taken to run a race

3. A column graph shows the number of pets owned by students: $0$ pets $\to 4$, $1$ pet $\to 9$, $2$ pets $\to 6$, $3$ pets $\to 2$.
   a) Which number of pets was most common?
   b) How many students owned $2$ pets?
   c) How many more students owned $1$ pet than $3$ pets?

4. A column graph shows the number of books read: Fantasy $7$, Mystery $5$, Sport $3$, Science $6$.
   a) Which category is greatest?
   b) How many students chose Science?
   c) How many students chose Fantasy and Mystery altogether?

5. A line graph shows daily temperatures: Monday ${18}^{\circ }\text{C}$, Tuesday ${20}^{\circ }\text{C}$, Wednesday ${19}^{\circ }\text{C}$, Thursday ${23}^{\circ }\text{C}$, Friday ${21}^{\circ }\text{C}$.
   a) On which day was the temperature highest?
   b) What was the temperature on Tuesday?
   c) What was the change from Wednesday to Thursday?

6. A line graph shows a plant's height over four weeks: Week 1 $12$ cm, Week 2 $15$ cm, Week 3 $17$ cm, Week 4 $20$ cm.
   a) What was the height in Week 3?
   b) Over which interval did the greatest increase occur?
   c) How much did the plant grow from Week 1 to Week 4?

7. A pie chart shows favourite lunch choices: sandwiches ${120}^{\circ }$, pasta ${90}^{\circ }$, sushi ${60}^{\circ }$, salad ${90}^{\circ }$.
   a) Which choice is most popular?
   b) Which two choices are equal in size?
   c) What fraction of the circle represents sushi?

8. A pie chart shows time spent on activities: sleeping ${150}^{\circ }$, school ${105}^{\circ }$, homework ${45}^{\circ }$, sport ${60}^{\circ }$.
   a) Which activity takes the largest part of the chart?
   b) What angle represents homework?
   c) What fraction of the circle represents sport?

9. Use the table to answer the questions.

a) Which month had the highest rainfall?
b) What was the rainfall in February?
c) How much rainfall was there altogether in January and April?

10. Use the table to answer the questions.

a) Which team had the most wins?
b) How many wins did Green have?
c) How many more wins did Blue have than Red?

Reasoning

11. Explain why favourite colour is categorical data but the number of siblings is numerical data.

12. Explain why mass is continuous data but the number of chairs in a room is discrete data.

13. A student says a pie chart is best for showing change over time. Explain why a line graph is usually more suitable.

14. A student reads a column graph but ignores the scale on the vertical axis. Explain why this can lead to an incorrect interpretation.

15. Explain why headings and units are important when interpreting a table.

Problem-solving

16. A survey records the transport used by students to travel to school. The answers are walk, bus, car and bike.

    Describe the type of data and state which display, a column graph or a line graph, would be more suitable.

17. The heights of plants are measured every week for $6$ weeks.

    Describe the type of data and state which display, a table or a line graph, would be more useful for showing the change over time.

18. A class records the number of goals scored by each player in a season.

    State whether the data is numerical, categorical, discrete or continuous, and explain a suitable display.

19. A pie chart shows that ${\displaystyle \frac{1}{2}}$ of students prefer soccer, ${\displaystyle \frac{1}{4}}$ prefer basketball and the rest prefer tennis.

    Which sport is least popular, and what fraction of students prefer tennis?

20. A table shows the number of visitors to a museum.

Use the table to determine:
a) the busiest day
b) the difference between Thursday and Monday
c) the total number of visitors on Tuesday and Wednesday

Potential Misunderstandings

• Thinking all data with words in the description must be categorical
• Confusing numerical data with discrete data, even though numerical data can be either discrete or continuous
• Thinking continuous data must contain decimals in the data shown
• Believing discrete data can take any value on a measurement scale
• Reading a graph without checking the title, labels or units
• Confusing the height of a column with the label underneath it
• Thinking a line graph should always be used, even when the data is categorical
• Misreading pie charts by comparing angles carelessly instead of using the size of the sectors
• Adding or comparing values incorrectly when reading from a table
• Ignoring the scale on axes when interpreting column graphs or line graphs