https://file.aiquickdraw.com/mathbot/file/1729454894307up4f8rvy.jpg

Let's solve this step-by-step.

### Original Salaries:  
591, 624, 787, 798, 803, 808, 902, **927**

Now, the salary **927** is changed to **791**. Let's analyze how this change affects both the **mean** and **median**.

---

## (a) Effect on the Mean:

The **mean** is the sum of all the salaries divided by the total number of salaries.

### Step 1: Calculate the original mean  
\[
\text{Sum of original salaries} = 591 + 624 + 787 + 798 + 803 + 808 + 902 + 927 = 6240
\]
\[
\text{Original Mean} = \frac{6240}{8} = 780
\]

### Step 2: Calculate the new mean  
When **927** is replaced by **791**, the new sum becomes:
\[
6240 - 927 + 791 = 6104
\]
\[
\text{New Mean} = \frac{6104}{8} = 763
\]

### Change in Mean:
\[
780 - 763 = 17
\]
So, the **mean decreases by 17 dollars**.

---

## (b) Effect on the Median:

The **median** is the middle value when all numbers are sorted in order. Since we have **8 salaries**, the median will be the **average of the 4th and 5th values**.

### Step 1: Original Median  
Original ordered salaries:  
591, 624, 787, 798, **803, 808**, 902, 927

The median is:
\[
\frac{798 + 803}{2} = \frac{1601}{2} = 800.5
\]

### Step 2: New Median  
When **927** is replaced by **791**, the new ordered salaries become:  
591, 624, 787, 791, **798, 803**, 808, 902

The new median is:
\[
\frac{798 + 803}{2} = 800.5
\]

### Change in Median:
The **median stays the same** at 800.5.

---

## Final Answers:
- **(a) What happens to the mean?**  
  It **decreases by 17 dollars**.

- **(b) What happens to the median?**  
  It **stays the same**.

---

Do you have any questions or need further clarification?

---

Here are 5 related questions to expand on this topic:
1. How does removing an outlier affect the mean and median?
2. What is the difference between the mean and the median in terms of sensitivity to changes?
3. How would the results change if the salary 927 were increased instead of decreased?
4. Why is the mean more sensitive to large changes than the median?
5. What happens to the range when the highest value in a dataset decreases?

**Tip:** For small datasets, changes in individual values can significantly impact the mean, but the median remains more stable.

The weekly salaries (in dollars) for 8 employees of a small business are given as 591, 624, 787, 798, 803, 808, 902, 927. Suppose that the $927 salary changes to $791. What happens to the mean and median?

Explore how changing a salary from $927 to $791 affects the mean and median of salaries for 8 employees. Learn the step-by-step calculations for determining changes in the mean and the stability of the median in this practical statistics problem. Suitable for middle school students.

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