The weekly salaries (in dollars) for 8 employees of a small business are given below. (Note that these are already ordered from least to greatest.) 662, 744, 772, 794, 797, 835, 902, 918 Send data to calculator Suppose that the $662 salary changes to $790. Answer the following. (a) What happens to the median? It decreases by O It increases by O It stays the same. (b) What happens to the mean? O It decreases by O It increases by O It stays the same.

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### How Changing a Value Affects the Mean and Median

#### Data Analysis and Probability

The weekly salaries (in dollars) for 8 employees of a small business are given below. (Note that these are already ordered from least to greatest.)

```
662, 744, 772, 794, 797, 835, 902, 918
```

You can send this data to the calculator by clicking on the "Send data to calculator" button.

---

Suppose that the $662 salary changes to $790. Answer the following:

(a) **What happens to the median?**
- It decreases by $\hspace{10mm}$
- It increases by $\hspace{10mm}$
- It stays the same.

(b) **What happens to the mean?**
- It decreases by $\hspace{10mm}$
- It increases by $\hspace{10mm}$
- It stays the same.

---

To submit your answers, click on the "Check" button.

You can also view an "Explanation" for more details.

---

**Explanation:**

When looking at changes to a set of data, it’s important to understand the impact on statistical measures such as the mean (average) and median (middle value).

For the given list:
- When a value in the list is changed, calculate the new median:
  - The median is the middle value(s) when the data is ordered. If the salary changes from $662 to $790, the new list will be: 744, 772, 790, 794, 797, 835, 902, 918. Median calculation should be revisited based on the new ordered list.
  
- Calculate the new mean:
  - The mean is the sum of all values divided by the number of values. Reassess the sum with the updated salary and divide by 8 to obtain the new mean.
Transcribed Image Text:### How Changing a Value Affects the Mean and Median #### Data Analysis and Probability The weekly salaries (in dollars) for 8 employees of a small business are given below. (Note that these are already ordered from least to greatest.) ``` 662, 744, 772, 794, 797, 835, 902, 918 ``` You can send this data to the calculator by clicking on the "Send data to calculator" button. --- Suppose that the $662 salary changes to $790. Answer the following: (a) **What happens to the median?** - It decreases by $\hspace{10mm}$ - It increases by $\hspace{10mm}$ - It stays the same. (b) **What happens to the mean?** - It decreases by $\hspace{10mm}$ - It increases by $\hspace{10mm}$ - It stays the same. --- To submit your answers, click on the "Check" button. You can also view an "Explanation" for more details. --- **Explanation:** When looking at changes to a set of data, it’s important to understand the impact on statistical measures such as the mean (average) and median (middle value). For the given list: - When a value in the list is changed, calculate the new median: - The median is the middle value(s) when the data is ordered. If the salary changes from $662 to $790, the new list will be: 744, 772, 790, 794, 797, 835, 902, 918. Median calculation should be revisited based on the new ordered list. - Calculate the new mean: - The mean is the sum of all values divided by the number of values. Reassess the sum with the updated salary and divide by 8 to obtain the new mean.
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