Ten scores have a mean = 9. If one score of 9 is removed, what is the mean for the remaining scores (4 points)?

Answer 1

I'm going to walk you through the logic of how you could figure this out, but the specific numbers used by this problem were picked to make the calculation easier.

There are two ways to think about this. We're doing the longer one first!

In order to calculate the mean, we must add all of our scores together and divide by n (the number of scores).

We know that the mean is 9. This tells us that the sum of all of our scores ÷ 10 is 9. We can also reverse this! The mean (9) multiplied by n (10) can tell us the overall sum of our scores (90).

From here, we can subtract 9 (giving us 81). Our number of scores has gone down by 1, making it 9, so now we divide 81 by 9. This gives us....... 9.

The mean score does not change!

Method 2:

If you are removing one score from the dataset and that score is equal to the mean, the mean will not change. That's it.

I hope this helps! Let me know if you would like some further clarification.