Impact on Mean

The mean is the average, so it takes every value into account.
When a new number is added, it shifts the balance toward itself.
A value below the current mean pulls it down, and a value above pulls it up.

A value equal to the current mean leaves it unchanged.
A value far from the mean — a high or low outlier — moves it more than a value that is close.
This is why one extreme number can noticeably change the mean.

Take the scores $70$, $80$, $90$, which have a mean of $80$.
Add a $60$: the new mean is $\frac{70 + 80 + 90 + 60}{4} = \frac{300}{4} = 75$.
The mean dropped from $80$ to $75$, pulled down by the low value.

Because the mean reacts strongly to extremes, it can be misleading when a dataset has an outlier.
One very high or very low value can drag the mean far from most of the data.
In such cases the median often describes the center better.

A class of 6 students has a mean score of $80$. A new student, Grace, scores $65$. Does the mean go up or down?
Grace's $65$ is below the current mean of $80$.
So including her score pulls the mean down.

The values $4$, $8$, $12$ have a mean of $8$. What is the new mean after adding $28$?
The new mean is $\frac{4 + 8 + 12 + 28}{4} = \frac{52}{4} = 13$.
The mean rose from $8$ to $13$, pulled up by the high value.

A dataset has a mean of $50$. You add one more value, also $50$. What happens to the mean?
The new value equals the current mean, so it does not pull it in either direction.
The mean stays at $50$.