A sample of n = 20 scores has a mean of M = 6. If one new person with a score of X = 27 is added to the sample, what will be the value for the new mean?

Mean = Σx/n

6 = Σx/20

Σx = 120

new Σx = 120 + 27 and new n = 21

Use the above equation to calculate new mean.

one sample has a mean of M= 4 and a second sample has a mean M=8. The two samples are combined into a single set of scores.

a. What is the mean for the combined set if both of the original samples have n= 7scores?
What is the mean for the combined set if the first sample has n= 3 and the second sample has n= 7?
What is the mean for the combined set if the first sample has n= 7 and the second sample has n= 3?

A sample of n=8 scores has a mean of M=12. What is the value of ƩX for this sample?

Well, adding a score of 27 to the mix certainly spices things up! Now, let's calculate the new mean with this addition.

We had a sample of 20 scores with a mean of 6. So, the sum of all the previous scores was 20 × 6 = 120.

When we add the new score of 27, the new sum becomes 120 + 27 = 147.

Since the sample size is now 21 (20 previous scores + 1 new score), we divide the new sum of 147 by 21 to find the new mean.

Doing this calculation, we get a fresh and juicy new mean of approximately 7.

So, after adding the impressive score of 27, the new mean value will be around 7. Keep up the good work, high-scoring friend!

To find the new mean after adding a new score to the sample, you need to calculate the sum of all scores and divide it by the total number of scores.

1. Start by finding the sum of the original 20 scores. Let's call this sum "sum_old".
2. Then, add the new score (X = 27) to the sum_old. This will give you the sum of all 21 scores, let's call this sum "sum_new".
3. Finally, divide the sum_new by the total number of scores (n + 1) to find the new mean.

Mathematically, the steps can be written as follows:

sum_old = n * M

sum_new = sum_old + X

New Mean = sum_new / (n + 1)

Let's plug in the given values:

sum_old = 20 * 6 = 120

sum_new = 120 + 27 = 147

New Mean = 147 / (20 + 1) = 147 / 21 = 7

Therefore, the new mean after adding a score of X = 27 will be 7.