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The five scores of two teams were recorded. Team A: 32, 35, 38, 40, 45. Team B: 20, 36, 38, 40, 56. Which statement is correct?

Competition practiceData & Probability
  • AThe two ranges are equal, so the two sets are equally spread out
  • BTeam B has the larger mean, because its highest score is the larger
  • CTeam B has the smaller range, because its three middle scores match Team A's
  • DThe two means are equal, but Team B has the larger range and the more spread-out scores

Step-by-Step Solution

Both teams total 190, so both means are 190 ÷ 5 = 38. The ranges differ sharply: Team A spans 45 − 32 = 13 while Team B spans 56 − 20 = 36. The mean deviation about the mean tells the same story — (6 + 3 + 0 + 2 + 7)/5 = 3.6 for Team A against (18 + 2 + 0 + 2 + 18)/5 = 8 for Team B. Equal means say nothing about spread, and a single very high score paired with a very low one can leave the mean untouched while stretching the range.
Answer: D) The two means are equal, but Team B has the larger range and the more spread-out scores

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