Two classes are not everyone
What we see in one or two groups may not hold for a much larger group.
A claim from one class
In a Grade 5 class, the girls have a mean height of 146.9 cm and the boys 142.94 cm.
Can we say “Girls are taller than boys” for all children in the country?
What this lesson covers
The idea
Patterns seen in data from only one or two groups cannot be generalised to everyone in a much larger group.
A claim from one class
In a Grade 5 class, the girls have a mean height of 146.9 cm and the boys 142.94 cm.
Can we say “Girls are taller than boys” for all children in the country?
- Yes, the data shows it
- No, one class is too small a group to decide
- Yes, if the girls are more in number
Test the claim
The claim is “Girls are taller than boys.” Look at the heights from two sections of Grade 5. Does each section agree with the claim?
One or two groups are not enough
Section A agrees with the claim: the girls are 3.96 cm taller on average. Section B goes against it: the boys are 1.91 cm taller on average.
So the data of one or two groups can point either way. We cannot generalise it to all children in the country, or around the world.
Patterns seen in data from only one or two groups cannot be generalised to everyone in a much larger group.
Notes
Patterns seen in data from only one or two groups cannot be generalised to everyone in a much larger group.
Check yourself
In Section A the girls’ mean height is more than the boys’. What can we say?
Two sections were measured. In one the girls are taller, in the other the boys. What should we conclude?
Which would help us say more about the heights of all children in the country?
Out of the 2 sections, in how many do the girls have the bigger mean height?
Answer: 1
Only Section A. In Section B the boys are taller.
- Girls are taller than boys in every class. One class cannot tell about every class. Section B shows the opposite.
- Every girl is taller than every boy. Not even in this class: the tallest student, 158 cm, is a boy.
- Girls are taller than boys in this class, on average — correct. Yes! This is about this class only, and about the mean.
- Two sections are not enough to decide for all children — correct. Yes! The data points in two directions and covers very few children.
- Girls are taller everywhere. The second section goes against this.
- Boys are taller everywhere. The first section goes against this.
- Heights of many children from many different places — correct. Yes! The larger and more varied the group measured, the safer it is to say something about everyone.
- Heights of the tallest class in one school. This is still one small group.
- Heights of the same class measured again. Measuring the same children again adds no new groups.