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The question asks to identify the correct effect of a 5% raise on the shape, median, and interquartile range (IQR) of the distribution of teacher salaries.

### Key concepts:
1. **Shape of the distribution**: A percentage increase (like a 5% raise) is a linear transformation that uniformly scales all values, meaning the overall shape of the distribution remains unchanged.
   
2. **Median**: The median will also increase by 5%, since it is a central measure of the data. In other words, the new median will be multiplied by 1.05.

3. **Interquartile Range (IQR)**: The IQR, which measures the spread of the middle 50% of the data, is also affected by a uniform percentage increase. The IQR will similarly be multiplied by 1.05.

### Correct answer:
- The shape will remain **unchanged**, the median will be **multiplied by 1.05**, and the IQR will be **multiplied by 1.05**.

This corresponds to the last option:
- **Shape – unchanged, Median – multiplied by 1.05, IQR – multiplied by 1.05**.

Would you like more details or have any other questions?

### Follow-up Questions:
1. How does a uniform increase affect other measures like the mean?
2. What would happen to the distribution if the raise was not uniform (e.g., varying by salary)?
3. How do different transformations affect the skewness of a distribution?
4. Why does the IQR scale in the same way as the median during a percentage increase?
5. How would the variance and standard deviation change in this case?

### Tip:
Remember, any percentage-based linear transformation affects all measures of center and spread uniformly, except for the shape, which remains unchanged.

A school system employs teachers at salaries between $38,000 and $70,000. The teachers' union and school board are negotiating the form of next years' increase in the salary schedule. Suppose that every teacher is given a 5% raise. Which of the following choices correctly describes the effect this raise will have on the shape, median, and interquartile range (IQR) of the resulting distribution of salary?

Explore how a 5% raise affects the shape, median, and interquartile range (IQR) of teacher salaries ranging from $38,000 to $70,000. This problem demonstrates the impact of uniform linear transformations on measures of center and spread, while maintaining the distribution shape.

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