A survey says 35% with a margin of error of 2%. What are the… Step by Step

Step by step

The question

Question: A survey says 35% with a margin of error of 2%.

What are the plausible values?

1 What the margin means

35% comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 2%, says how far it can be.

35% ± 2%

± means plus or minus: we go 2% down and 2% up.

The true value is likely in between.

± = plus or minus

true value: likely within 2% of 35%

2 Lowest and highest

The lowest likely value: 35% minus 2% is 33%.

lowest = 35% − 2% = 33%

The highest: 35% plus 2% is 37%.

highest = 35% + 2% = 37%

3 Draw it

A number line from 32 to 38: a bit of room on each side.

The likely values go from 33% to 37%.

We colour them green.

35%, the sample's answer, is right in the middle.

4 Say the range

So the plausible values go from 33% to 37%.

= 33% to 37%

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 33% to 37% is 4%.

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

So it is right!

37% − 33% = 4% = 2 × 2%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: say the range.

Last: check.

Answer