tenequal scores have a mean of 30. if one score is doubled, and the other nine remain the same, what is the mean of the new set of scores?

It would ordinarily depend upon which score is doubled, but since they are all the same, each score must originally be 30. The combined total now becomes 330, and the mean becomes 33.

To find the mean of the new set of scores, we need to calculate the sum of all the scores and divide it by the number of scores.

Let's assume the initial ten scores are represented by x1, x2, ..., x10. We are given that their mean is 30, so we can write the equation:

(x1 + x2 + ... + x10) / 10 = 30

If one score, let's say x1, is doubled, we will have the new set of scores as follows: 2x1, x2, x3, ..., x10.

Now, let's find the sum of the new set of scores:

(2x1 + x2 + ... + x10)

We can rewrite this sum as follows:

(2x1 + x2 + ... + x10) = 2x1 + (x2 + ... + x10) = 2x1 + (x1 + x2 + ... + x10 - x1) = 2x1 + (x1 + x2 + ... + x10) - x1

Since (x1 + x2 + ... + x10) is simply the sum of the original ten scores, we can substitute it with 10 * 30, which is the sum of the initial scores:

2x1 + (x1 + x2 + ... + x10) - x1 = 2x1 + 10 * 30 - x1

Simplifying further:

2x1 + 10 * 30 - x1 = x1 + 300

So, the sum of the new set of scores is x1 + 300.

Now, we can find the mean of the new set of scores by dividing the sum by the number of scores, which is still 10:

Mean = (x1 + 300) / 10

Therefore, the mean of the new set of scores, when one score is doubled and the other nine remain the same, is (x1 + 300) / 10.