The mean of 9 numbers is 42. A 10th number is added to the list, and the mean of all 10 numbers becomes 44. What is the value of the 10th…

The total of the first 9 numbers is $9 \times 42 = 378$. After adding a 10th number, the mean is 44, so the new total is $10 \times 44 = 440$. The added number is the difference: $440 - 378 = 62$. Check: $\frac{378 + 62}{10} = 44$. A common wrong answer is 44, which comes from assuming the new number equals the new mean, and another is 86, found by taking $44 + 2 \cdot 21$ or otherwise guessing. A third is 2, the change in the mean, which ignores that the change is spread across ten values. Always work with totals rather than averages.