A sample of n=7 score has mean M=5.After a new score is added to the sample the mean is found to be M=6.What is the new value of the score (Hint:compare the value for £X before and after the score was added)
7*5+ x = 8*6
To find the new value of the score, we can use the formula for calculating the mean:
mean = (sum of all scores) / (number of scores)
Given that n=7 scores have a mean of M=5, we can set up the equation:
5 = (sum of the 7 scores) / 7
Multiplying both sides by 7, we get:
35 = sum of the 7 scores
Now, let's add the new score. After adding the new score, the mean becomes M=6. We can set up the new equation:
6 = (sum of the 8 scores) / 8
Multiplying both sides by 8, we get:
48 = sum of the 8 scores
To find the new value of the score, we need to find the difference between the sum of the 8 scores and the sum of the original 7 scores:
48 - 35 = 13
Therefore, the new value of the score is 13.
To find the new value of the score, we can use the formula for the mean of a sample. The mean (M) is calculated by summing up all the scores and dividing by the total number of scores.
Step 1: Calculate the sum of the scores before the new score was added:
Sum of scores before = M * n = 5 * 7 = 35
Step 2: Calculate the sum of scores after the new score was added:
Sum of scores after = M * (n+1) = 6 * (7+1) = 6 * 8 = 48
Step 3: Calculate the value of the new score:
New score = Sum of scores after - Sum of scores before
New score = 48 - 35
New score = 13
Therefore, the new value of the score is 13.