068. Data Types and Data Collection

Learning Intentions

• To know the meaning of the terms primary source, secondary source, census, sample and observation
• classify variables as numerical (discrete or continuous) or categorical
• To understand that different methods are suitable for collecting different types of data, based on the size and nature of the data

Pre-requisite Summary

• Understand that data is information collected to answer a question
• Know that a variable is something that can change from one case to another
• Be able to distinguish between counting and measuring
• Understand that categories group items by type or label
• Know that a population is the full group being studied
• Understand that practical limits such as time, cost and access affect how data is collected

Worked Examples

Worked Example 1

For each term, state its meaning and give an example:
a) primary source
b) secondary source
c) observation

Worked Example 2

For each term, state its meaning and give an example:
a) census
b) sample
c) explain one advantage of each

Worked Example 3

Classify each variable as categorical, numerical discrete, or numerical continuous:
a) favourite sport
b) number of siblings
c) height of a student

Worked Example 4

Classify each variable as categorical, numerical discrete, or numerical continuous:
a) eye colour
b) number of pets
c) time taken to run $100$ m

Worked Example 5

Choose a suitable method of collecting data and justify it:
a) finding the shoe sizes of all students in one class
b) finding the daily temperature at noon for a month
c) finding the favourite music genre of students in a school of $1200$ students

Worked Example 6

A researcher wants data on the mass of apples sold at a market.
a) State whether the variable is categorical, numerical discrete, or numerical continuous.
b) Suggest a suitable method of collection.
c) Explain whether a census or sample is more suitable.

Problems

Problem 1

For each term, state its meaning and give an example:
a) primary source
b) secondary source
c) observation

Problem 2

For each term, state its meaning and give an example:
a) census
b) sample
c) explain one advantage of each

Problem 3

Classify each variable as categorical, numerical discrete, or numerical continuous:
a) favourite fruit
b) number of books read in a month
c) arm span of a student

Problem 4

Classify each variable as categorical, numerical discrete, or numerical continuous:
a) hair colour
b) number of cars in a household
c) amount of water in a bottle

Problem 5

Choose a suitable method of collecting data and justify it:
a) finding the hand spans of all students in one class
b) finding rainfall each day for two weeks
c) finding the favourite school subject of students in a school of $900$ students

Problem 6

A researcher wants data on the lengths of leaves in a garden.
a) State whether the variable is categorical, numerical discrete, or numerical continuous.
b) Suggest a suitable method of collection.
c) Explain whether a census or sample is more suitable.

Exercises

Understanding and Fluency

1. Match each term to its meaning:
   a) primary source
   b) secondary source
   c) observation

2. State whether each example is a primary or secondary source:
   a) measuring the heights of your classmates
   b) using a government report
   c) recording the colour of cars passing a school gate

3. State whether each study uses a census or a sample:
   a) surveying every student in one class
   b) surveying $50$ students from a school of $1000$
   c) measuring every tree in a small garden

4. Classify each variable:
   a) type of pet
   b) number of goals scored
   c) temperature of a drink

5. Classify each variable:
   a) brand of phone
   b) number of siblings
   c) distance travelled to school

6. Classify each numerical variable as discrete or continuous:
   a) number of text messages sent
   b) mass of a watermelon
   c) time spent doing homework

7. Choose a suitable method for collecting each type of data:
   a) favourite lunch food of a class
   b) height of tomato plants over time
   c) number of buses arriving in one hour

8. Choose whether a census or sample is more suitable:
   a) finding the favourite colour of a class of $25$ students
   b) finding the favourite streaming service of all teenagers in Australia
   c) finding the heights of all players in one netball team

Reasoning

9. Explain why the number of siblings is numerical discrete and not continuous.

10. A student says that height is numerical discrete because it can be written as a decimal. Explain the mistake.

11. Explain why a school might use a sample instead of a census when surveying all students.

12. A student says that favourite sport is numerical because you can count how many people choose each sport. Explain why this is incorrect.

Problem-solving

13. A class wants to find the most popular fruit among students.
    a) State the variable.
    b) Classify the variable.
    c) Suggest a suitable collection method.

14. A weather station records the temperature every hour for one day.
    a) State the variable.
    b) Classify the variable.
    c) State whether observation is a suitable method.

15. A sports club wants to know the average number of training sessions attended each week by its members.
    a) State the variable.
    b) Classify it.
    c) Suggest whether a census or sample is more suitable and explain.

16. A researcher wants to know the masses of fish in a large lake.
    a) Classify the variable.
    b) Suggest a suitable collection method.
    c) Decide whether a census or sample is more realistic.

17. A school library records the number of books borrowed by each student in a term.
    a) State the variable.
    b) Classify it.
    c) Explain why the variable is not categorical.

18. A council studies the colour of cars parked in a shopping centre.
    a) State the variable.
    b) Classify it.
    c) Suggest whether direct observation is suitable.

Potential Misunderstandings

• Students may confuse primary and secondary sources by focusing on where the data is written rather than where it originally came from
• Students may think a sample and a census are the same because both involve collecting data
• Students may think any numerical variable is continuous
• Students may think any variable that can be counted from responses is numerical, even when the responses are categories
• Students may confuse discrete data with rounded continuous data
• Students may assume a census is always better, without considering time, cost and practicality
• Students may choose an unsuitable method of collection because they do not consider the size or nature of the data
• Students may think observation can only be used for categorical data, even though it can also be used to record numerical data in some contexts

Next: 069. Summarising Numerical Data