A survey says 52% with a margin of error of 3%. Is 50% a plausible… Step by Step

Step by step

The question

Question: A survey says 52% with a margin of error of 3%.

Is 50% a plausible value?

1 What the margin means

52% 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.

52% ± 3%

± means plus or minus: we go 3% down and 3% up.

The true value is likely in between.

± = plus or minus

true value: likely within 3% of 52%

2 Lowest and highest

The lowest likely value: 52% minus 3% is 49%.

lowest = 52% − 3% = 49%

The highest: 52% plus 3% is 55%.

highest = 52% + 3% = 55%

3 Draw it

A number line from 47 to 57: a bit of room on each side.

The likely values go from 49% to 55%.

We colour them green.

52%, the sample's answer, is right in the middle.

Now 50%, the value in the question.

We mark it in red.

4 Inside or outside

50% is between 49% and 55%: inside the green part.

= 49% ≤ 50% ≤ 55%

Careful!

Plausible means likely.

It does not mean the true value is 50% for sure.

Careful: plausible = likely, not sure

So yes: 50% is a plausible value.

= yes, 50% is plausible

5 Check

Let's check another way: how far is 50% from 52%?

52% minus 50% is 2%.

That is within the margin, 3%.

So it is right!

52% − 50% = 2%, 2% ≤ 3%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer