Consider two data sets.
Set A: n = 5; x = 7
Set B: n = 50; x = 7
(a)
Suppose the number 38 is included as an additional data value in Set A. Compute 
x
 for the new data set. Hint: 

x = nx.
 To compute 
x
 for the new data set, add 38 to 

x
 of the original data set and divide by 6. (Round your answer to two decimal places.)

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.

Consider two data sets. Set A: n = 5; x = 7. Set B: n = 50; x = 7. (a) Suppose the number 38 is included as an additional data value in Set A. Compute x for the new data set. Hint: x = nx. To compute x for the new data set, add 38 to x of the original data set and divide by 6. (Round your answer to two decimal places.)

Learn how to compute the new mean for Set A after adding a new value, using the mean formula. Set A initially has n = 5 and mean x̄ = 7. We add 38 to the set and find the updated mean, rounded to two decimal places. This problem is suitable for students in Grades 6-8 and covers key concepts in statistics and averages.

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