A sample has a mean of M 40 If a score of X 55 is removed from the sample then the sample mean will increase
No, decrease.
Mean = ∑x/n
To determine if the sample mean will increase when a specific score is removed, we need to calculate the new mean for the modified sample. Here's how you can do that:
1. Start by calculating the sum of all the scores in the original sample. Let's assume there are 'n' scores in the sample.
2. Multiply the original mean (M) by the total number of scores in the sample (n) to get the sum of all the scores. So, the sum of the original sample is M * n.
3. Next, subtract the score that will be removed (X) from the sum calculated in step 2. Let's call this new sum 'new_sum'.
new_sum = (M * n) - X
4. Determine the new number of scores in the modified sample. Since one score has been removed, we subtract 1 from the original number of scores (n) to get the new number of scores (n-1).
5. Finally, calculate the new mean (new_M) by dividing the new sum (new_sum) by the new number of scores (n-1).
new_M = new_sum / (n - 1)
Now, compare the original mean (M) with the new mean (new_M):
- If new_M is greater than M, then the sample mean will increase when the score X is removed.
- If new_M is equal to M, then the sample mean will remain the same.
- If new_M is less than M, then the sample mean will decrease when the score X is removed.
In your case, you mentioned that the original mean is 40 (M = 40) and a score of 55 (X = 55) is removed. Use the steps above to calculate the new mean and compare it to the original mean to determine if it increases.