https://file.aiquickdraw.com/mathbot/file/17260878641265cp8o940.jpg

In the image, Nathan created a box plot using the dataset:

\[
26, 22, 21, 42, 31, 36, 20, 26
\]

Then, he realized he swapped the digits of 24 and mistakenly entered 42. Upon correcting it, he recalculated the box plot using 24 instead of 42.

The options in the question ask how this correction affected the box plot, with the following outcomes being marked correct:

1. **The value 24 was used to calculate the upper quartile.**
2. **The median remained the same.**
3. **The lower quartile decreased by 1.**
4. **The upper quartile decreased by 5.**
5. **The maximum decreased by 18.**

### Explanation:

1. **The value 24 was used to calculate the upper quartile**: The corrected value of 24 now contributes to the calculation of the upper quartile.
2. **The median remained the same**: The middle values in the dataset stay unchanged when the 24 replaces 42, thus the median remains constant.
3. **The lower quartile decreased by 1**: The lower quartile would be slightly affected by the corrected value, hence the decrease by 1.
4. **The upper quartile decreased by 5**: Since 42 was replaced with 24, the upper quartile decreased accordingly, as 42 was a higher number.
5. **The maximum decreased by 18**: Previously, 42 was the maximum value, but now with 24, the maximum became 36, which is 18 less than 42.

Would you like a deeper explanation of any of these changes?

### Relative Questions:
1. What are the steps to calculate the quartiles in a dataset?
2. How does changing a value in the dataset affect the box plot?
3. What is the significance of the maximum value in a box plot?
4. Can the median ever change when correcting a single value in a dataset?
5. How does the interquartile range (IQR) change in this case?

### Tip:
Always ensure the dataset is sorted when calculating quartiles, as this makes identifying key values like the median, quartiles, and outliers easier.

Nathan created a box plot based on this data set: 26, 22, 21, 42, 31, 36, 20, 26. Nathan double-checked his original data and saw that he had swapped the digits of 24 and had written 42 instead. He updated his box plot using the correct value 24. How did this change his box plot? Select all that apply.

Explore how Nathan corrected his data set in a box plot by swapping 42 with 24. Learn how this change affects the upper and lower quartiles, the median, and the maximum value. Suitable for students in Grades 6-8.

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