Mean and Median

Considering the salary for an upcoming job is a very important part of the decision making process for selecting a new position or career. 

Suppose the Jones Corporation posted the following salaries for ten full-time employees:

Choose one • 10 points

     **Employee Name**

                  **Yearly Salary**

Brandon

$45,000

Robert

$58,000

Chloe

$62,000

Andrew

$59,000

David

$70,000

Tanya

$84,000

Rodney

$49,000

Sally


$67,000

Manuel

$78,000

Alexis

$68,000
 
**1. In looking at this grouping of salaries, what salary might be expected for an open position based on the mean of these listed?**

**2. Sometimes, the median can generate a different expectation for the salary an employee can expect when working at a position in the corporation. What is the median salary for the salaries listed above?**

Let's calculate the mean and median salaries for the Jones Corporation based on the provided salaries.

### Mean Salary

To calculate the mean salary, we sum up all the salaries and then divide by the number of employees.

**Salaries:**
- Brandon: $45,000
- Robert: $58,000
- Chloe: $62,000
- Andrew: $59,000
- David: $70,000
- Tanya: $84,000
- Rodney: $49,000
- Sally: $67,000
- Manuel: $78,000
- Alexis: $68,000

**Sum of salaries:**
\[ 45,000 + 58,000 + 62,000 + 59,000 + 70,000 + 84,000 + 49,000 + 67,000 + 78,000 + 68,000 \]

\[ = 640,000 \]

**Number of employees:**
\[ 10 \]

**Mean salary:**
\[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Employees}} \]

\[ \text{Mean} = \frac{640,000}{10} = 64,000 \]

So, the expected salary for an open position based on the mean is $64,000.

### Median Salary

To calculate the median salary, we need to list the salaries in ascending order and then find the middle value. If there is an even number of observations, the median is the average of the two middle numbers.

**Salaries in ascending order:**
- $45,000
- $49,000
- $58,000
- $59,000
- $62,000
- $67,000
- $68,000
- $70,000
- $78,000
- $84,000

**Middle values (5th and 6th):**
- 5th value: $62,000
- 6th value: $67,000

**Median salary:**
\[ \text{Median} = \frac{62,000 + 67,000}{2} \]

\[ \text{Median} = \frac{129,000}{2} = 64,500 \]

So, the median salary for the salaries listed is $64,500.

### Summary

1. **Mean Salary:** $64,000
2. **Median Salary:** $64,500

Both the mean and median are quite close, providing a consistent expectation of around $64,000 to $64,500 for an open position in the Jones Corporation.

Do you want details or have any questions about these calculations?

Here are five more questions you might want to explore:

1. How does the range of salaries affect the mean and median?
2. What would the mean and median be if a new salary of $100,000 was added?
3. How would the removal of the highest salary impact the mean and median?
4. Can you calculate the standard deviation of these salaries?
5. How does the distribution of these salaries compare to a normal distribution?

**Tip:** When considering job offers, it’s useful to compare both the mean and median salaries, as they can provide different perspectives on what you might expect to earn.

Learn how to calculate the mean and median salaries for employees of Jones Corporation. Understand the difference between mean and median and their implications for salary expectations. Suitable for high school students and professionals interested in statistics and data analysis.

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