A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found to be M = 6. What is the value of the new score? (Hint: Compare the values for ƩX before and after the score was added.

Well, it seems like one of those times where a new score just waltzes in and changes everything! So, let's see what we can figure out.

We know that the sample of n = 7 scores has a mean of M = 5. So, the sum of those original 7 scores must be 7 x 5 = 35.

Now, after adding in the new score, the mean becomes M = 6. That means the sum of all 8 scores is now 8 x 6 = 48.

But hold on a second, where did that new score come from? If we subtract the original sum (35) from the new sum (48), we get 13. So, the value of the new score must be 13.

So, that new score really came in like a heavyweight champion, making quite the impact!

To find the value of the new score, we need to compare the sum of the scores before and after the new score was added.

Let's denote the sum of the original 7 scores as ƩX_1 and the sum of the new 8 scores (including the new score) as ƩX_2.

According to the problem, the original 7 scores have a mean (M_1) of 5. Therefore, the sum of the original 7 scores (ƩX_1) can be calculated by multiplying the mean by the number of scores:
ƩX_1 = M_1 * n
= 5 * 7
= 35

After adding the new score, the total number of scores becomes 8. The mean of the new 8 scores (M_2) is 6. Therefore, the sum of the new 8 scores (ƩX_2) can be calculated by multiplying the mean by the number of scores:
ƩX_2 = M_2 * (n + 1)
= 6 * 8
= 48

The difference between ƩX_2 and ƩX_1 represents the value of the new score:
New score = ƩX_2 - ƩX_1
= 48 - 35
= 13

Therefore, the value of the new score is 13.

To find the value of the new score, let's first determine the sum of the scores before and after the new score was added.

The sum of scores before the new score was added is given by the formula ƩX = n * M, where n is the number of scores and M is the mean. In this case, the sum before adding the new score is 7 * 5 = 35.

Now, let's consider the sum of scores after the new score was added. We know that the mean after adding the new score is 6. Since there are now n + 1 scores, the sum after adding the new score is (n + 1) * M. So, the sum of scores after adding the new score is (7 + 1) * 6 = 48.

To find the value of the new score, we need to find the difference between the sum after adding the new score and the sum before adding the new score. Therefore, the new score is 48 - 35 = 13.

Hence, the value of the new score is 13.

Mean = sum/n

5 = sum/7

5(7) = 7(sum/7)

35 = sum

35 to 42

42-35 = 7