Grade 7 Statistics: Compare Populations

Compare two data sets

What You'll Learn

Compare two data sets by their means and medians
Compare spread with the range and MAD

📖Comparing

To compare two groups, find each group's center (mean or median) and subtract. Compare spread with the range. When both groups have the same mean absolute deviation (MAD), divide the difference of the means by the MAD to see how far apart the groups really are.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Quiz scores — Class A: 13, 6, 8, 4, 19; Class B: 10, 14, 4, 5, 13. How much greater is the median score of Class B than the median score of Class A?
1. Class B in order: 4, 5, 10, 13, 14 — the middle number is 10.
2. Class A in order: 4, 6, 8, 13, 19 — the middle number is 8.
3. Subtract the medians: 10 − 8 = 2.
Answer: 2
Example 2
Minutes spent on homework — Group A: 24, 27, 29, 32, 32, 24; Group B: 26, 21, 18, 18, 23, 26. Both data sets have a mean absolute deviation (MAD) of 3. The difference between the means is how many times the MAD?
1. Mean of Group A: (24 + 27 + 29 + 32 + 32 + 24) ÷ 6 = 168 ÷ 6 = 28.
2. Mean of Group B: (26 + 21 + 18 + 18 + 23 + 26) ÷ 6 = 132 ÷ 6 = 22.
3. The means differ by 28 − 22 = 6.
4. Divide by the MAD: 6 ÷ 3 = 2, so the means are 2 MADs apart.
Answer: 2
Example 3
Points scored in their games — Hawks: 55, 28, 44, 34, 35; Eagles: 49, 42, 32, 52, 26. How much greater is the median score of Eagles than the median score of Hawks?
1. Eagles in order: 26, 32, 42, 49, 52 — the middle number is 42.
2. Hawks in order: 28, 34, 35, 44, 55 — the middle number is 35.
3. Subtract the medians: 42 − 35 = 7.
Answer: 7