A company decides to give all employees a $2000 raise no matter their current salary. Select **all** the correct responses below. 

The raise will cause the mean salary to increase by $2000. 

The raise will cause the median salary to increase by $2000. 

The raise will cause the coefficient of variation in salary to decrease. 

The raise will cause the variance in salary to increase. 

Let's analyze each statement:

1. **The raise will cause the mean salary to increase by $2000.**
   - **True.** Since every employee receives a $2000 raise, the mean salary will increase by $2000 as the raise is applied uniformly across all employees.

2. **The raise will cause the median salary to increase by $2000.**
   - **True.** The median is the middle value in an ordered list of salaries. Adding $2000 to each salary shifts the entire distribution, so the median will also increase by $2000.

3. **The raise will cause the coefficient of variation in salary to decrease.**
   - **True.** The coefficient of variation (CV) is the ratio of the standard deviation to the mean. Since the $2000 raise increases the mean without affecting the spread (variance) significantly, the CV will decrease because the mean is rising while the relative dispersion remains the same.

4. **The raise will cause the variance in salary to increase.**
   - **False.** Variance measures the spread of data points around the mean. A constant shift (like adding $2000 to every salary) does not change the relative spread of the salaries, so the variance remains unchanged.

### Correct responses:
- The raise will cause the mean salary to increase by $2000.
- The raise will cause the median salary to increase by $2000.
- The raise will cause the coefficient of variation in salary to decrease.

Do you want details or have any questions?

Here are 5 related questions for further exploration:
1. How would the standard deviation of the salaries be affected by a fixed raise for all employees?
2. What happens to the interquartile range when a constant value is added to all data points?
3. How does a percentage-based raise affect the mean and variance of salaries?
4. If bonuses are awarded based on a percentage of current salary, how would that impact the coefficient of variation?
5. What are other statistical measures that remain unchanged after adding a constant to all data points?

**Tip:** The variance and standard deviation only change when the relative distances between data points change. Adding or subtracting the same constant to all data points only shifts the entire distribution without changing its spread.

A company decides to give all employees a $2000 raise no matter their current salary. Select all the correct responses below.

The raise will cause the mean salary to increase by $2000.

The raise will cause the median salary to increase by $2000.

The raise will cause the coefficient of variation in salary to decrease.

The raise will cause the variance in salary to increase.

Explore how a uniform $2000 raise affects the mean, median, coefficient of variation, and variance of salaries. This analysis covers key statistical concepts, including measures of central tendency and dispersion. Suitable for students in Grades 11-12.

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