A sample has a mean of M = 25. If one person with a score of X = 25 is added to the sample, what effect will it have on the sample mean?

Nothing.

@ Ms. Sue, your answer is nothing? can you explain why the effect is nothing? I'm not understanding.

The new person's score is the same as the mean; therefore the mean will not be affected.

To understand the effect of adding a person with a score of X = 25 to the sample, we need to consider how the sample mean is calculated.

The sample mean, denoted as M, is obtained by summing up all the scores in the sample and then dividing by the number of individuals in the sample. Mathematically, it can be represented as:

M = (X1 + X2 + X3 + ... + Xn) / n

Where X1, X2, X3, ..., Xn represents the individual scores in the sample, and n represents the number of individuals in the sample.

In this case, since the mean M is given as 25, we know that the sum of all the scores in the sample divided by the number of individuals in the sample equals 25.

Now, when we add one more person with a score of X = 25 to the sample, the new sample mean (let's call it M') can be obtained by incorporating this new data point in the calculation.

The new sum of all the scores in the sample will be: (X1 + X2 + X3 + ... + Xn + X)

And the new sample size will be: (n + 1)

Therefore, the new sample mean M' will be:

M' = (X1 + X2 + X3 + ... + Xn + X) / (n + 1)

In this case, since X = 25, the new sample mean can be written as:

M' = (X1 + X2 + X3 + ... + Xn + 25) / (n + 1)

So, adding a person with a score of X = 25 to the sample will increment the sum of scores by 25 and increase the sample size by 1. The resulting effect on the sample mean will depend on the values of X1, X2, X3, ..., Xn, and the new mean M' can be calculated using the formula provided.

Note: Without additional information about the scores X1, X2, X3, ..., Xn, we cannot determine the specific value of the new mean M'.