What number is removed from a data set of fifteen numbers with a mean of eight, resulting in a new mean of six?

To find the correct number that was removed from the data set, let's first determine the total sum of the original fifteen numbers. Given that the mean of those numbers is eight, we can calculate the total sum by multiplying the mean by the count of numbers:

Total sum of the original data set = Mean × Number of values = 8 × 15 = 120.

Now, when a number is removed, the mean of the remaining fourteen numbers becomes six. We can again calculate the total sum of the remaining numbers:

Total sum of the remaining data set = New Mean × Number of remaining values = 6 × 14 = 84.

To find the value of the number that was removed, we subtract the total sum of the remaining numbers from the total sum of the original numbers:

Number removed = Total sum of the original data set - Total sum of the remaining data set = 120 - 84 = 36.

Thus, the number that was removed from the dataset, resulting in the new mean, is 36. This confirms that the answer is indeed accurate.