There is variation everywhere. No two objects are exactly alike. 

Often we would like to measure the amount of variation but this can be tricky.

Here we are trying to measure the maths abilities of a group of students.

We want to see this real variation but our view can be obscured by other forms of variation.

Every individual is different.
Natural variation is the variation that occurs from individual to individual. 
This is sometimes called individual-to-individual variation or real variation.

This is the variation we want to measure.

For the Year 9 students above, what is the true ability of each student in maths?
What inaccuracies might be introduced if we are not careful about how we measure this ability?

Examples for the maths ability measuring process:

• A poorly designed test that had too many hard questions or questions not about maths.

• A marker who did not know how to mark the test.

• Multiple markers who marked differently - some were strict (their students got low scores) and some were lenient (their students got high scores).

• Marks getting recorded incorrectly.
  
  

Other examples

• Some people will have an increased heart rate when this is being measured in a public setting.

• The growth of a plant in a laboratory will be different from that of one growing in the wild.

This is variation caused by the effect of a particular 'situation'. 

Other examples

• A person who has just run to the classroom for the lesson will have a higher heart rate than normal.

• The weight of an animal will be affected by how recently it has eaten.

• A student who did not get enough sleep the night before will have a slower reaction time than usual.

This is variation that we see when sampling a population.

Sometimes we will already have access to a selection of data (Secondary data) that we can use in an investigation. If the dataset is large enough we do not have to use all of it to produce a reasonable analysis for our investigation. We can simply take a sample of this and analyze that instead.

For large populations, samples are likely going to be different. In order for us to minimize the effect of sampling variation on our analysis we simply need to take a large enough sample. For most of our purposes the minimum sample size will be 100.

We also need to make sure that our sample isn't biased towards certain outcomes. Our sample needs to be representative of the population we are referring back to. In most cases, we can prevent bias in a sample by taking a simple random sample.

In general, sampling variation is managed by:

1. Taking a large enough sample size(minimum of 100).

2. Performing a simple random sample.

Link to padlet examples