The average of 7 numbers is 49. If each number is decreased by 4, what will…

The average (mean) of a group of numbers is (sum of all the numbers) divided by (how many numbers there are). Because of this definition, a fixed rule holds: if the same amount is added to, or subtracted from, every single number in a group, the average changes by exactly that same amount, since the total sum changes by (count of numbers x that amount), and dividing by the count leaves the change unchanged.

1. The average of 7 numbers is given as 49, so their total sum = 7 x 49 = 343.

2. Each of the 7 numbers is decreased by 4, so the total sum decreases by 7 x 4 = 28.

3. New sum = 343 - 28 = 315.

4. New average = new sum / count = 315 / 7 = 45.

Cross-check using the rule directly: new average = old average - (amount subtracted from each number) = 49 - 4 = 45, which matches the sum-based calculation above.

So the new average is 45.