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Two families with 6 members are randomly selected. Each of the family members took an IQ test. Their scores are as follows. Which of the two families has more consistent scores?

Family A: 109, 113, 117, 120, 128, 111
Family B: 120, 118, 115, 116, 119, 118

(1 point)
Responses

The scores of both families are equally consistent.
The scores of both families are equally consistent.

Family B is more consistent, because the range of their scores is higher than that of Family A.
Family B is more consistent, because the range of their scores is higher than that of Family A.

Family B is more consistent, because the range of their scores is lower than that of Family A.
Family B is more consistent, because the range of their scores is lower than that of Family A.

Family A is more consistent, because the range of their scores is lower than that of Family B.

1 answer

To determine which family has more consistent scores, we can look at the range of each family's IQ scores. The range is calculated as the difference between the highest and lowest scores.

Family A Scores:
109, 113, 117, 120, 128, 111

  • Lowest score = 109
  • Highest score = 128
  • Range = 128 - 109 = 19

Family B Scores:
120, 118, 115, 116, 119, 118

  • Lowest score = 115
  • Highest score = 120
  • Range = 120 - 115 = 5

Comparison of Ranges:

  • Family A has a range of 19.
  • Family B has a range of 5.

Since a lower range indicates more consistency in scores, we can conclude that Family B has more consistent scores.

Therefore, the correct response is:

Family B is more consistent, because the range of their scores is lower than that of Family A.