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Comparing two data sets worksheets

Two groups have means of 14 and 18. Is four a lot? Nothing about that number answers the question until you know how much the data varies anyway — and that is the whole of this sheet. These free printable worksheets ask for the gap between two centers measured in the sets' own spread.

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Comparing two data sets
Comparing two data sets worksheet — Two sets of five, one shared MAD, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Every pair on these sheets has the same mean absolute deviation, and the sheet says so at the top. That is not a simplification, it is the condition the standard names: two distributions can only be compared this way when their variabilities are similar. With one shared MAD there is one unit to measure the gap in, and the answer is a whole number of them.

Why this sheet works

The work is three things and the answer key prints all three: the mean of A, the mean of B, and the difference divided by the MAD. A child who stops after the subtraction has done the arithmetic and not the comparison — the difference is a number about these two sets, and the multiple is a number you can carry to any other pair.

How this one works

How many MADs apart are the two means?

A:11 + 14 + 20 + 26 + 29 = 100, ÷ 5 =20
A:11 + 14 + 20 + 26 + 29 = 100, ÷ 5 =20
B:20 + 29 + 32 + 35 + 44 = 160, ÷ 5 =32
A:11 + 14 + 20 + 26 + 29 = 100, ÷ 5 =20
B:20 + 29 + 32 + 35 + 44 = 160, ÷ 5 =32
32 − 20 =12
32 − 20 =12
MAD = 6, so 12 ÷ 6 =2
  1. Find each set's mean first — that is the one number standing for where the set SITS. Start with A.
  2. Now B's mean, the same way.
  3. B sits 32 − 20 = 12 above A. On its own that number says nothing: 12 is a lot for data packed tightly together and very little for data spread wide.
  4. So measure the gap in the sets' OWN spread. Both have a MAD of 6, so the two means are 12 ÷ 6 = 2 MADs apart — the centres differ by 2 times as much as the values typically differ from their own centre.

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