Compare MAD: class A 70, 80, 90; class B 78, 80, 82 Step by Step

Step by step

The question

Question: compare the MAD of class A, 70, 80, 90, and class B, 78, 80, 82.

class A: 70, 80, 90

= class B: 78, 80, 82

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 class A

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

The sum is 240.

There are 3 numbers.

240 divided by 3 is 80.

= mean of class A = 70 + 80 + 903 = 2403 = 80

The distances from 80: 10, 0, 10.

= distances: 10, 0, 10

They add up to 20.

Divided by 3: 6.7.

= MAD = 203 ≈ 6.7

2 MAD of class B

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

The sum is 240.

There are 3 numbers.

240 divided by 3 is 80.

= mean of class B = 78 + 80 + 823 = 2403 = 80

The distances from 80: 2, 0, 2.

= distances: 2, 0, 2

They add up to 4.

Divided by 3: 1.3.

= MAD = 43 ≈ 1.3

Careful!

The question is about spread.

So we compare the MADs, not the means.

Careful: compare the spread, not the mean

3 Compare

1.3 is smaller.

So class B is closer together: more consistent.

= 6.7 > 1.3 → class B is closer together

4 Check

Let's check with the lists: class A goes from 70 to 90.

class B goes from 78 to 82.

class B is more bunched up.

So the answer is right!

class A: 70 to 90, class B: 78 to 82

Let's look back.

First: mAD of class A.

Then: mAD of class B.

Then: compare.

Last: check.

Answer