A poll says 51% with a margin of error of 4%. What are the plausible… Step by Step

Step by step

The question

Question: A poll says 51% with a margin of error of 4%.

What are the plausible values?

1 What the margin means

51% comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 4%, says how far it can be.

51% ± 4%

± means plus or minus: we go 4% down and 4% up.

The true value is likely in between.

± = plus or minus

true value: likely within 4% of 51%

2 Lowest and highest

The lowest likely value: 51% minus 4% is 47%.

lowest = 51% − 4% = 47%

The highest: 51% plus 4% is 55%.

highest = 51% + 4% = 55%

3 Draw it

A number line from 45 to 57: a bit of room on each side.

The likely values go from 47% to 55%.

We colour them green.

51%, the sample's answer, is right in the middle.

4 Say the range

So the plausible values go from 47% to 55%.

= 47% to 55%

Careful!

The true value is likely in this range.

We can't be sure where.

Careful: plausible = likely, not sure

5 Check

Let's check: from 47% to 55% is 8%.

That is 4% down and 4% up: 2 times 4%.

So it is right!

55% − 47% = 8% = 2 × 4%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: say the range.

Last: check.

Answer