10.01 Data collection
Introduction
Statistical data can be divided two types, categorical and numerical.
Categorical data
Data that is collected as a set of words is called categorical data.
Imagine asking someone for their favourite colour, country of birth, or gender. Their answer would always be a word. We can also think of categorical data as values which can be sorted into groups or categories.
Examples
Example 1
A class was surveyed about where they went on their most recent holiday. What kind of data are the survey results?
Categorical data is made up of words.
- Examples include: favourite country, types of pet owned, mode of transport, and preferred film genre.
Numerical data
When the data is a set of numbers, it is called numerical data.
Imagine asking someone for their height, their age, how many pets they own, or how long they spend on social media each day. Their answers would always be a number.
Numerical data is divided into two types, continuous and discrete.
Discrete numerical data is counted, so its values are separated. If you asked someone to tell you their shoe size they might say "10", they might even say "10 and a half", but they would not say "10 and seven sixteenths". If you have to count to find the answer, the data is discrete.
Examples
Example 2
All the students in your school take a survey with the four questions below. Which two will have discrete numerical data as their results?
Numerical data is made up of two types:
- Discrete numerical data is counted.
- Examples include: number of pets owned, number of books read, population of a city, and goals scored in a season.
- Continuous numerical data is measured.
- Examples include: Height of a person, weight of an animal, length of a movie, and time taken to run a race.
Data collection
We get the best data from a census because it includes the entire population. However, it's not always possible to conduct a census, so we often get our data from surveys instead.
When we take a survey it is important that the results are representative of the population. This means that the results that we get for any question we ask of the survey would be the same as if we asked it of a census. This also means that the mean, median, mode and range of the survey should be very close to the same results of the census (although getting exactly the same results is almost impossible).
If a survey is not representative, we call it biased. There are a number of potential sources of bias that we should avoid:
Consider who is being surveyed. If the people being surveyed do not resemble the population, the survey is likely to be biased. For example, surveying train travellers about their opinions on public transport will likely give very different results than a census of the entire population.
Also consider how many people are being surveyed. Asking one person's opinion will not tell you anything about anyone else's opinion. In general, the bigger the number of people being surveyed, the closer the results will be to a census.
Make sure that the questions being asked actually address the question at hand. For example, asking, "Do you approve of the current governing party?" does not give the same results as asking, "Will you vote for the current governing party in the next election?"
Avoid questions which use emotive language or might otherwise influence the results of the survey. For example, asking, "Do you watch the most popular sport, soccer?" will be biased unlike asking, "Do you watch soccer?". These are referred to as "leading questions" as they lead the person being surveyed to a particular answer.
Once we have collected data we need to find a way to organise and display it.
Examples
Example 3
Consider the survey question and the sample and determine whether the outcomes are likely to be biased or not.
Yvonne is asking people on her soccer team, "What's your favourite sport?"
Lachlan randomly selected people from his school to find about the school sports. He asked, "What's your favourite school sport?"
Tricia randomly selected people from her school and asked, "The local AFL team is donating money to our school this term. What's your favourite sport?"
Example 4
Which one of the following data types is discrete?
Example 5
Classify this data into its correct category: Weights of kittens
Example 6
What type of data is each of the following:
The time spent watching TV each day.
Favourite TV show.
There are a number of potential sources of bias that we should avoid:
Consider who is being surveyed. If the people being surveyed do not resemble the population, the survey is likely to be biased.
Also consider how many people are being surveyed. Asking one person's opinion will not tell you anything about anyone else's opinion.
Make sure that the questions being asked actually address the question at hand.
Avoid questions which use emotive language or might otherwise influence the results of the survey.