https://file.aiquickdraw.com/mathbot/file/1726013588641fe7xuhqi.jpg

The image presents a boxplot summarizing Angela's sales for 12 days, with the following multiple-choice question:

- **Question:** Angela sold 70 items the next day she worked, and 70 is added to the original data set. Which statements would be true of the new boxplot?

**The statements given are:**
- a. The value of the median of the boxplot increases. (Marked correct)
- b. The value of the upper extreme of the boxplot increases.
- c. The range of the boxplot decreases. (Marked incorrect)
- d. The value of the upper quartile of the boxplot decreases.

### Let's analyze these:
1. **Median (a):** Adding a high number like 70 to the dataset would likely increase the median, assuming this new number pushes the median higher. This makes **a** true, as marked.
  
2. **Upper extreme (b):** The maximum value is now 70, which was previously lower. This would increase the upper extreme of the boxplot, so **b** should also be true (although it's not marked as such in the image).

3. **Range (c):** The range is the difference between the maximum and minimum values. Since the new maximum is 70, the range increases rather than decreases, making **c** false, as marked.

4. **Upper quartile (d):** Adding a large value like 70 could increase the upper quartile (Q3), not decrease it, making **d** false.

The key concept here is how adding an extreme value affects the median, quartiles, and overall range of a boxplot.

Would you like to dive deeper into this topic or explore another related concept?

Here are 5 related questions you might consider:
1. How does adding an extreme outlier affect the quartiles in a boxplot?
2. How is the interquartile range (IQR) calculated, and what does it represent?
3. What is the significance of the median in a boxplot?
4. How would removing the lowest value in the dataset affect the boxplot?
5. How does the range compare to the IQR when analyzing the spread of data?

**Tip:** Adding extreme values to a dataset can significantly affect the spread (range and IQR), especially if the new value is much higher or lower than the existing data.

Angela sold 70 items the next day she worked, and 70 is added to the original data set. Which statements would be true of the new boxplot?

Understand how adding new data, like Angela's 70 sales, affects a boxplot's median, upper extreme, range, and quartiles. Learn the impacts on measures of central tendency and spread, suitable for Grades 6-8 students.

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