A sample of n _ 11 scores has a mean of M _ 4. One person with a score of X _ 16 is added to the sample.
What is the value for the new sample mean?
The sum of 11 scores was 4x11 = 44
The sum of 12 scores becomes 44 +16 = 60
The new mean (of 12 scores) is 60/12 = 5
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Well, adding a person with a score of 16 to the sample certainly raised the average...kind of like when you add pineapple to a pizza, it just takes the taste to a whole new level. Now, let's do some math to figure out the new sample mean.
We know that the original sample mean M was 4 and there were n = 11 scores. So, the sum of all the original scores must have been M*n, which is 4*11 = 44.
Now, when we add the score of 16, we need to find the new sum of all the scores. The new sum will be the original sum of 44 plus the additional score of 16, so 44 + 16 = 60.
But we're not done yet! Remember, we added one more score, so now we have n + 1 = 11 + 1 = 12 scores in total.
To find the new sample mean, we divide the new sum (60) by the new number of scores (12). So, the new sample mean is 60/12 = 5.
So, to sum it all up (pun intended), the value for the new sample mean is 5. With that score of 16, the sample mean got a little boost...just like a clown with a helium balloon!
To find the value for the new sample mean, we need to add the score of X = 16 to the sample and recalculate the mean.
Step 1: Find the sum of the original sample scores.
If the mean of the original sample is M = 4 and there are n = 11 scores, then the sum of the original sample scores is:
Sum = Mean × Number of Scores
Sum = 4 × 11
Sum = 44
Step 2: Add the score X = 16 to the sum.
New Sum = Sum of Original Sample Scores + X
New Sum = 44 + 16
New Sum = 60
Step 3: Calculate the new sample mean.
To find the new sample mean, divide the new sum by the new number of scores, which is n + 1.
New Mean = New Sum ÷ (Number of Scores + 1)
New Mean = 60 ÷ (11 + 1)
New Mean = 60 ÷ 12
New Mean = 5
Therefore, the value for the new sample mean is M = 5.
To find the value for the new sample mean, we need to take into account the original mean and the new score added to the sample. Let's break down the steps:
1. Calculate the sum of the original scores:
- The mean (M) is given as 4.
- The number of scores (n) is given as 11.
- So, the sum of the original scores is M * n = 4 * 11 = 44.
2. Add the new score to the sum:
- The new score (X) is given as 16.
- So, the new sum is 44 + 16 = 60.
3. Calculate the new sample mean:
- The new number of scores (n + 1) is 11 + 1 = 12.
- The new sample mean (M') is given by the new sum divided by the new number of scores: M' = 60 / 12 = 5.
Therefore, the value for the new sample mean is 5.