In a sample of n = 6 scores,the smallest score is X = 3,the largest score is X = 10,and the mean is M = 6.If the largest score is changed from X = 10 to X = 22,then what is the value of the new mean?
A)The mean is still M = 6
B)The mean is M = 7
C)The mean is M = 8
D)Cannot be determined from the information given

Question

Quizplus · Accepted Answer

To find the new mean, we need to use the formula for the mean:
M = (sum of all scores) / n

Initially, we know that the smallest score is X = 3, the largest score is X = 10, and the mean is M = 6. We can use this information to find the sum of all scores:
sum = n * M = 6 * 6 = 36

Now, if we change the largest score from X = 10 to X = 22, the new sum of all scores will be:
new sum = old sum - old largest score + new largest score
new sum = 36 - 10 + 22
new sum = 48

And the new number of scores is still n = 6, so we can calculate the new mean:
new M = new sum / n
new M = 48 / 6
new M = 8

Therefore, the new mean is M = 8, and the correct answer is C).

In a Sample of N = 6 Scores,the Smallest Score