A poll says 61% with a margin of error of 5%. Is 58% a plausible… Step by Step

Step by step

The question

Question: A poll says 61% with a margin of error of 5%.

Is 58% a plausible value?

1 What the margin means

61% comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 5%, says how far it can be.

61% ± 5%

± means plus or minus: we go 5% down and 5% up.

The true value is likely in between.

± = plus or minus

true value: likely within 5% of 61%

2 Lowest and highest

The lowest likely value: 61% minus 5% is 56%.

lowest = 61% − 5% = 56%

The highest: 61% plus 5% is 66%.

highest = 61% + 5% = 66%

3 Draw it

A number line from 52 to 70: a bit of room on each side.

The likely values go from 56% to 66%.

We colour them green.

61%, the sample's answer, is right in the middle.

Now 58%, the value in the question.

We mark it in red.

4 Inside or outside

58% is between 56% and 66%: inside the green part.

= 56% ≤ 58% ≤ 66%

Careful!

Plausible means likely.

It does not mean the true value is 58% for sure.

Careful: plausible = likely, not sure

So yes: 58% is a plausible value.

= yes, 58% is plausible

5 Check

Let's check another way: how far is 58% from 61%?

61% minus 58% is 3%.

That is within the margin, 5%.

So it is right!

61% − 58% = 3%, 3% ≤ 5%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer