A survey says 64% with a margin of error of 2%. Is 61% a plausible… Step by Step

Step by step

The question

Question: A survey says 64% with a margin of error of 2%.

Is 61% a plausible value?

1 What the margin means

64% 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.

64% ± 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 64%

2 Lowest and highest

The lowest likely value: 64% minus 2% is 62%.

lowest = 64% − 2% = 62%

The highest: 64% plus 2% is 66%.

highest = 64% + 2% = 66%

3 Draw it

A number line from 60 to 67: a bit of room on each side.

The likely values go from 62% to 66%.

We colour them green.

64%, the sample's answer, is right in the middle.

Now 61%, the value in the question.

We mark it in red.

4 Inside or outside

61% is below 62%: outside the green part.

= 61% < 62%

Careful!

Close is not enough.

It must be inside the margin of error.

Careful: not 61% is close to 64% → plausible ✗

So no: 61% is not a plausible value.

= no, 61% is not plausible

5 Check

Let's check another way: how far is 61% from 64%?

64% minus 61% is 3%.

That is more than the margin, 2%.

So it is right!

64% − 61% = 3%, 3% > 2%

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: inside or outside.

Last: check.

Answer