Which list yields a mean of 76.6?

• A. 74, 82, 78, 72, 78, 73, 78, 72, 78, 81
• B. 74, 82, 78, 72, 73, 78, 72, 78, 81
• C. 70, 80, 78, 72, 76, 74, 77, 79, 83
• D. 75, 83, 77, 71, 79, 73, 80, 70, 76, 82

Answer: (A)

The mean is found by adding all the numbers together and dividing by how many numbers there are. For the first list, the sum is 74+82+78+72+78+73+78+72+78+81 = 766, and there are 10 numbers, so the mean is 766/10 = 76.6, which matches the target.

The second list has nine numbers with a total of 688, giving a mean of 688/9 ≈ 76.44, not 76.6. The third list also has nine numbers, totaling 689, so the mean is 689/9 ≈ 76.56, not exactly 76.6 (it rounds to 76.6 if you round to one decimal, but the exact mean isn’t 76.6). The fourth list contains ten numbers that also sum to 766, so its mean is 766/10 = 76.6 exactly.

So the first list yields the target mean, and another list does as well.