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Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Understanding Box-and-Whisker Plots**

The box-and-whisker plot below represents some data set. What is the value of the first quartile?

![Box-and-Whisker Plot]

This box-and-whisker plot provides a visual representation of the spread and center of a data set. Let's break down what this plot shows:

1. **Whiskers**: The lines extending from the edges of the box to the smallest and largest values, which are not outliers.
2. **Box**: The box itself shows the interquartile range (IQR), which is the range from the first quartile (Q1) to the third quartile (Q3).
3. **Median Line**: Inside the box, there's a line that represents the median (Q2) of the data.

### Key Points to Identify on the Plot:
- The **first quartile (Q1)** is the value at the edge of the box closer to the lower set of the data. 
- The **median (Q2)** is the middle value of the data, represented by the line inside the box.
- The **third quartile (Q3)** is the value at the edge of the box closer to the higher set of data.
- The **min and max values** are represented by the ends of the whiskers.

### To Find the First Quartile:
Examine the plot and identify where the left edge of the box is located. Based on the plot provided, the first quartile (Q1) value lies between 25 and 50, specifically at 25.

**Answer:** 
\( \boxed{25} \)

This value indicates that 25% of the data values fall below this point.
Transcribed Image Text:**Understanding Box-and-Whisker Plots** The box-and-whisker plot below represents some data set. What is the value of the first quartile? ![Box-and-Whisker Plot] This box-and-whisker plot provides a visual representation of the spread and center of a data set. Let's break down what this plot shows: 1. **Whiskers**: The lines extending from the edges of the box to the smallest and largest values, which are not outliers. 2. **Box**: The box itself shows the interquartile range (IQR), which is the range from the first quartile (Q1) to the third quartile (Q3). 3. **Median Line**: Inside the box, there's a line that represents the median (Q2) of the data. ### Key Points to Identify on the Plot: - The **first quartile (Q1)** is the value at the edge of the box closer to the lower set of the data. - The **median (Q2)** is the middle value of the data, represented by the line inside the box. - The **third quartile (Q3)** is the value at the edge of the box closer to the higher set of data. - The **min and max values** are represented by the ends of the whiskers. ### To Find the First Quartile: Examine the plot and identify where the left edge of the box is located. Based on the plot provided, the first quartile (Q1) value lies between 25 and 50, specifically at 25. **Answer:** \( \boxed{25} \) This value indicates that 25% of the data values fall below this point.
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