https://file.aiquickdraw.com/mathbot/file/17270447988951n7rfvfd.jpg

Let's break down the scenario described in the image and how correcting the data affects the box plot.

### Original dataLet's break down the scenario described in the image and how correcting the data affects the box plot.

### Original 
- **Data Set**: 26, 22, 21, 42, 21, 36, 20, 26

Nathan realizes he incorrectly wrote 42 instead of 24. The correct data set should be:
- **Corrected Data Set**: 26, 22, 21, 24, 21, 36, 20, 26

### Box Plot Analysis:
1. **Maximum Decreases**: The original maximum was 42, which decreases to 36 after correcting the error (since 36 is now the largest value).
   - ✔ The maximum decreased by 18 (42 − 24 = 18).

2. **Upper Quartile (Q3)**: 
   - Before correction, the third quartile would have been calculated based on the value 42, but now it is calculated based on 24. This likely lowers the upper quartile.
   - ✔ The upper quartile decreased by 5.

3. **Median (Q2)**: 
   - The median is the middle value. The median likely remained the same because swapping the digits only affects the higher values.
   - ✔ The median remained the same.

4. **Lower Quartile (Q1)**:
   - The lower quartile (first quartile) is based on the lower part of the data. Since the error was in the higher values, the lower quartile decreases slightly.
   - ✔ The lower quartile decreased by 1.

5. **Value of 24 Used in Calculating the Upper Quartile**: 
   - ✔ The value 24 replaced 42 and was now used in calculating the upper quartile, affecting its calculation.

### Conclusion:
- **Correct Answers**:
  - The maximum decreased by 18.
  - The upper quartile decreased by 5.
  - The median remained the same.
  - The lower quartile decreased by 1.
  - The value 24 was used to calculate the upper quartile.

Would you like to go over how box plots are calculated in more detail or have any questions about the quartiles?

Here are 5 related questions you can explore:
1. How do you calculate the median in a dataset?
2. What effect does outlier removal have on a box plot?
3. How are quartiles used to detect data spread?
4. How do you calculate interquartile range (IQR)?
5. How does changing a single data point affect the overall statistics?

**Tip**: When updating data points, always recheck the extremes (minimum, maximum) and quartiles, as these are sensitive to changes in the dataset!

Nathan created a box plot based on this data set:
26, 22, 21, 42, 21, 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.

Understand how correcting an error in a data set affects a box plot. Learn how the maximum, upper quartile, lower quartile, and median change when the value 42 is corrected to 24. This detailed analysis is perfect for students in Grades 6-8 studying statistics and data representation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation