Compare MAD: shop A 10, 12, 14; shop B 8, 12, 16 Step by Step

Step by step

The question

Question: compare the MAD of shop A, 10, 12, 14, and shop B, 8, 12, 16.

shop A: 10, 12, 14

= shop B: 8, 12, 16

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 shop A

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

The sum is 36.

There are 3 numbers.

36 divided by 3 is 12.

= mean of shop A = 10 + 12 + 143 = 363 = 12

The distances from 12: 2, 0, 2.

= distances: 2, 0, 2

They add up to 4.

Divided by 3: 1.3.

= MAD = 43 ≈ 1.3

2 MAD of shop B

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

The sum is 36.

There are 3 numbers.

36 divided by 3 is 12.

= mean of shop B = 8 + 12 + 163 = 363 = 12

The distances from 12: 4, 0, 4.

= distances: 4, 0, 4

They add up to 8.

Divided by 3: 2.7.

= MAD = 83 ≈ 2.7

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 shop A is closer together: more consistent.

= 1.3 < 2.7 → shop A is closer together

4 Check

Let's check with the lists: shop A goes from 10 to 14.

shop B goes from 8 to 16.

shop A is more bunched up.

So the answer is right!

shop A: 10 to 14, shop B: 8 to 16

Let's look back.

First: mAD of shop A.

Then: mAD of shop B.

Then: compare.

Last: check.

Answer