The mean score in a sample is 78 points with a margin of error of 6… Step by Step

Step by step

The question

Question: The mean score in a sample is 78 points with a margin of error of 6 points.

What are the plausible values for the mean?

1 What the margin means

78 points comes from a sample: only some of the people.

The true value for everyone can be a bit different.

The margin of error, 6 points, says how far it can be.

78 ± 6

± means plus or minus: we go 6 points down and 6 points up.

The true value is likely in between.

± = plus or minus

true value: likely within 6 of 78

2 Lowest and highest

The lowest likely value: 78 minus 6 is 72.

lowest = 78 − 6 = 72

The highest: 78 plus 6 is 84.

highest = 78 + 6 = 84

3 Draw it

A number line from 68 to 88: a bit of room on each side.

The likely values go from 72 to 84.

We colour them green.

78, the sample's answer, is right in the middle.

4 Say the range

So the plausible values go from 72 points to 84 points.

= 72 points to 84 points

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 72 to 84 is 12.

That is 6 down and 6 up: 2 times 6.

So it is right!

84 − 72 = 12 = 2 × 6

Let's look back.

First: what the margin means.

Then: lowest and highest.

Then: draw it.

Then: say the range.

Last: check.

Answer