Compare MAD: team A 2, 4, 6, 8, 10; team B 5, 6, 6, 7, 6 Step by Step

Step by step

The question

Question: compare the MAD of team A, 2, 4, 6, 8, 10, and team B, 5, 6, 6, 7, 6.

team A: 2, 4, 6, 8, 10

= team B: 5, 6, 6, 7, 6

The MAD says how spread out the numbers are.

A smaller MAD means the numbers are closer together.

smaller MAD = closer together

1 MAD of team A

Team A: the mean is the sum divided by how many.

The sum is 30.

There are 5 numbers.

30 divided by 5 is 6.

= mean of team A = 2 + 4 + 6 + 8 + 105 = 305 = 6

The distances from 6: 4, 2, 0, 2, 4.

= distances: 4, 2, 0, 2, 4

They add up to 12.

Divided by 5: 2.4.

= MAD = 125 = 2.4

2 MAD of team B

Team B: the mean is the sum divided by how many.

The sum is 30.

There are 5 numbers.

30 divided by 5 is 6.

= mean of team B = 5 + 6 + 6 + 7 + 65 = 305 = 6

The distances from 6: 1, 0, 0, 1, 0.

= distances: 1, 0, 0, 1, 0

They add up to 2.

Divided by 5: 0.4.

= MAD = 25 = 0.4

Careful!

The question is about spread.

So we compare the MADs, not the means.

Careful: compare the spread, not the mean

3 Compare

0.4 is smaller.

So team B is closer together: more consistent.

= 2.4 > 0.4 → team B is closer together

4 Check

Let's check with the lists: team A goes from 2 to 10.

team B goes from 5 to 7.

team B is more bunched up.

So the answer is right!

team A: 2 to 10, team B: 5 to 7

Let's look back.

First: mAD of team A.

Then: mAD of team B.

Then: compare.

Last: check.

Answer