Step by step
The question
Question: A poll says 48% with a margin of error of 3%.
What are the plausible values?
1 What the margin means
48% comes from a sample: only some of the people.
The true value for everyone can be a bit different.
The margin of error, 3%, says how far it can be.
± means plus or minus: we go 3% down and 3% up.
The true value is likely in between.
2 Lowest and highest
The lowest likely value: 48% minus 3% is 45%.
The highest: 48% plus 3% is 51%.
3 Draw it
A number line from 43 to 53: a bit of room on each side.
The likely values go from 45% to 51%.
We colour them green.
48%, the sample's answer, is right in the middle.
4 Say the range
So the plausible values go from 45% to 51%.
Careful!
The true value is likely in this range.
We can't be sure where.
5 Check
Let's check: from 45% to 51% is 6%.
That is 3% down and 3% up: 2 times 3%.
So it is right!
Let's look back.
First: what the margin means.
Then: lowest and highest.
Then: draw it.
Then: say the range.
Last: check.