This option is correct because the arithmetic mean of two numbers is obtained by adding them and dividing by 2. Here, (10 + 20) ÷ 2 = 30 ÷ 2 = 15. This value lies exactly midway between 10 and 20. Therefore, the arithmetic mean is 15.
Option A:
Taking 10 as the mean would ignore the contribution of the larger number 20. The average must be between the two numbers and balanced by both. Since 10 is at the lower end, it cannot be the mean of 10 and 20.
Option B:
A value of 12 is between 10 and 20 but does not satisfy the mean formula. Using (10 + 20) ÷ 2 does not produce 12. Therefore, this number does not represent the correct arithmetic mean.
Option C:
20 is the larger of the two numbers and would be the mean only if both numbers were 20. Because the other number is 10, the mean must lie between 10 and 20, not at the greater endpoint. Thus, 20 is incorrect.
Option D:
The average 15 comes directly from the formula for mean and is equidistant from 10 and 20. It balances the two values, which is the key idea of an arithmetic mean. Hence, this option correctly answers the question.
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