The original average of Set A is $\bar{x} = 7$, and there are $n = 5$ data points. The sum of the original data values in Set A is:

$\text{Sum of Set A} = \bar{x} \times n = 7 \times 5 = 35$

When we add the number 38 to the set, the new total sum becomes:

$\text{New sum} = 35 + 38 = 73$

The number of data points in the new set is $n = 6$, so the new mean $\bar{x}_{\text{new}}$ is:

$\bar{x}_{\text{new}} = \frac{73}{6} \approx 12.17$

Thus, the new mean of Set A is approximately 12.17.

Do you have any questions or want more details?

Here are 5 related questions for further exploration:

1. What happens to the mean if a smaller number, like 2, is added instead of 38?
2. How does the mean of Set B change if you add 38?
3. What is the effect of adding a number much larger than the current mean to a data set?
4. If the number 38 was added to Set B, how much would the mean change?
5. How would you calculate the new variance after adding 38 to Set A?

Tip: Adding a number larger than the current mean increases the mean; adding a smaller number decreases it.