https://file.aiquickdraw.com/mathbot/file/1727189549648xnqh0ma6.jpg


Two more employees, with annual salaries of 
45,000 and 48,000
, join the sales department. What is the effect of the salaries of the two new employees on the box plot, and why

The image you provided shows a box plot representing the salaries of employees in the sales department, where salaries range from 20,000 to 40,000 dollars, with key features like the minimum, maximum, quartiles, and median highlighted.

Two new employees with salaries of 45,000 and 48,000 dollars join the department. These salaries are above the current maximum of 40,000.

### Effects on the box plot:
1. **Increase in the maximum value**: The addition of these two higher salaries will shift the maximum value of the box plot from 40,000 to 48,000.
2. **No change in the quartiles or median**: The quartiles (Q1, Q2/median, and Q3) likely won't change significantly because the new salaries are outliers, much higher than the existing data. These quartiles are more influenced by the bulk of the data (central data points), not extreme values.
3. **Potential outliers**: The new salaries might be considered outliers if they fall far enough outside the typical range of the other data points, especially since they are well above the current range.
4. **Adjustment of whiskers**: The right-hand whisker (upper bound) will extend to cover the new maximum value of 48,000. The whiskers in a box plot typically represent the range within 1.5 times the interquartile range (IQR). The new points may be beyond this, marking them as outliers.

### Why?
- The box plot summarizes data using five key values: minimum, Q1, median, Q3, and maximum. The addition of two values above the current maximum alters only the maximum and possibly introduces outliers, without impacting the central distribution (median and quartiles) much, unless they cause the IQR to change drastically.

Would you like more details on how the quartiles and outliers are calculated? 

Here are some related questions for further exploration:

1. How do you calculate outliers using the interquartile range (IQR)?
2. How would adding lower salaries affect the box plot?
3. Can the median value change if more data is added?
4. How would you compute the exact IQR from the given data?
5. What is the significance of outliers in a dataset?

**Tip**: Outliers can significantly affect statistical analyses, so always check their influence when adding new data.

Two more employees, with annual salaries of 45,000 and 48,000, join the sales department. What is the effect of the salaries of the two new employees on the box plot, and why?

Understand the impact of adding two high salaries (45,000 and 48,000 dollars) on the box plot representing sales department salaries. Explore how the maximum value, outliers, and whiskers of the box plot change while the median and quartiles remain unaffected. Suitable for students in Grades 9-12.

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