Outliers and clusters

An outlier is a data value that is much higher or much lower than the rest of the data.
It doesn’t seem to “fit” with the other numbers.

Example:
Data set: 12, 13, 14, 15, 35

• Most numbers are close together around 12–15.

• 35 is much larger — it’s an outlier.

In real life: If most students score between 60–80 on a test, but one student scores 100, that 100 is an outlier.

A cluster is a group of data values that are close together. They form a “bunch” or group when you look at a graph or list.

Example:
Data set: 10, 11, 12, 12, 13, 25, 26, 27

• There’s a cluster around 10–13.

• There’s another cluster around 25–27.

In real life: If you record the ages of people at a theme park, you might see clusters around 10–15 years (children) and around 30–40 years (parents).

surveying and sampling

A survey is a way of collecting information by asking questions or recording data from people.

Example:
If you ask everyone in your class what their favourite sport is — you’re doing a survey.

In real life: Surveys are used to find out things like:

• What foods students like in the canteen

• How people plan to vote in an election

• How many hours people spend on social media

A sample is a small group taken from a larger population (the whole group you’re interested in).
We use sampling when it’s too hard or too time-consuming to ask everyone.

Example:
If your school has 800 students, but you only survey 100 of them about their favourite subject — those 100 students are your sample.

Why we sample:

• Saves time

• Saves money

• Still gives a good idea about the larger group (if chosen fairly)