Comparing two data sets, step by step
Two groups have means of 14 and 18.
The question
How many MADs apart are the two means?
How many MADs apart are the two means?
A:30 + 30 + 31 + 32 + 37 = 160, ÷ 5 =32
A:30 + 30 + 31 + 32 + 37 = 160, ÷ 5 =32
B:32 + 35 + 36 + 38 + 39 = 180, ÷ 5 =36
A:30 + 30 + 31 + 32 + 37 = 160, ÷ 5 =32
B:32 + 35 + 36 + 38 + 39 = 180, ÷ 5 =36
36 − 32 =4
36 − 32 =4
MAD = 2, so 4 ÷ 2 =2
- Find each set's mean first — that is the one number standing for where the set SITS. Start with A.
- Now B's mean, the same way.
- B sits 36 − 32 = 4 above A. On its own that number says nothing: 4 is a lot for data packed tightly together and very little for data spread wide.
- So measure the gap in the sets' OWN spread. Both have a MAD of 2, so the two means are 4 ÷ 2 = 2 MADs apart — the centres differ by 2 times as much as the values typically differ from their own centre.
How it works.
- 01
Find each set's mean first — that is the one number standing for where the set SITS. Start with A.
- 02
Now B's mean, the same way.
- 03
B sits 36 − 32 = 4 above A. On its own that number says nothing: 4 is a lot for data packed tightly together and very little for data spread wide.
- 04
So measure the gap in the sets' OWN spread. Both have a MAD of 2, so the two means are 4 ÷ 2 = 2 MADs apart — the centres differ by 2 times as much as the values typically differ from their own centre.