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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

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

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

1 answer

To determine which family has more consistent scores, we can calculate the range of scores for each family. The range is calculated as the difference between the highest and lowest scores.

Family A Scores:

  • Scores: 109, 113, 117, 120, 128, 111
  • Highest Score: 128
  • Lowest Score: 109
  • Range = 128 - 109 = 19

Family B Scores:

  • Scores: 120, 118, 115, 116, 119, 118
  • Highest Score: 120
  • Lowest Score: 115
  • Range = 120 - 115 = 5

Now comparing the ranges:

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

Since Family B has a lower range, it indicates that the scores are more clustered around the mean and, therefore, more consistent.

Thus, the correct response would be:

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