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 calculated to be M = 6.The new score was X = 13.

Question

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 calculated to be M = 6.The new score was X = 13.​

Quizplus · Accepted Answer

To find if the answer is true or false, we can use the formula for finding the new mean:

New Mean = (Sum of all scores + New score) / (Number of scores + 1)

We know the original mean (M = 5) and the new mean (M = 6), and one of the scores in the sample (X = 13). We also know the number of scores in the original sample was 7.

Using the formula and plugging in the values we know:

6 = (Sum of all scores + 13) / 8

Multiplying both sides by 8:

48 = Sum of all scores + 13

Subtracting 13 from both sides:

35 = Sum of all scores

To check if this is correct, we can calculate the original mean:

M = (Sum of all scores) / (Number of scores)

M = 35 / 7 = 5

So the original mean was 5, which matches what we were given. Therefore, the answer is true.

A Sample of N = 7 Scores Has a Mean