A survey says 55% with a margin of error of 4%. Is 50% a plausible… Step by Step

Step by step

The question

Question: A survey says 55% with a margin of error of 4%.

Is 50% a plausible value?

1 What the margin means

55% 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.

55% ± 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 55%

2 Lowest and highest

The lowest likely value: 55% minus 4% is 51%.

lowest = 55% − 4% = 51%

The highest: 55% plus 4% is 59%.

highest = 55% + 4% = 59%

3 Draw it

A number line from 48 to 62: a bit of room on each side.

The likely values go from 51% to 59%.

We colour them green.

55%, 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 below 51%: outside the green part.

= 50% < 51%

Careful!

Close is not enough.

It must be inside the margin of error.

Careful: not 50% is close to 55% → plausible ✗

So no: 50% is not a plausible value.

= no, 50% is not plausible

5 Check

Let's check another way: how far is 50% from 55%?

55% minus 50% is 5%.

That is more than the margin, 4%.

So it is right!

55% − 50% = 5%, 5% > 4%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer