The arithmetic mean of a set of 50 numbers is 38.If the two numbers,45 and 55,are discarded,the mean of the remaining set of numbers is__.

The mean is the total divided by how many there are. So, the new mean is

(50*38-45-55)/48 = 37.5

To find the mean of the remaining set of numbers, we need to calculate the sum of the remaining numbers and divide it by the count of those numbers.

First, let's find the sum of the original set of numbers. We know that the mean of the set of 50 numbers is 38. By multiplying the mean (38) by the count (50), we can find the sum of the original set: 38 * 50 = 1900.

To find the sum of the remaining set of numbers, we need to subtract the sums of the two discarded numbers (45 and 55) from the sum of the original set. The sum of the discarded numbers is 45 + 55 = 100.

Now, we can calculate the sum of the remaining set by subtracting the sum of the discarded numbers from the sum of the original set: 1900 - 100 = 1800.

Finally, to find the mean of the remaining set, we divide the sum of the remaining set by the count of the remaining numbers. Since we discarded two numbers, the count of the remaining set is 50 - 2 = 48.

Therefore, the mean of the remaining set of numbers is 1800 / 48 = 37.5.