The box-and-whisker plot shows the average temperatures in Orlando, Florida in January. Which statement about the temperatures in Orlando must be true? A. About half of the days in January had average temperatures above 75 degrees. B. About 50% of the days in January had average temperatures between 66 and 75 degrees. C. The coldest day in January was 66 degrees. D. The hottest day in December was 75 degree

Elementary Geometry For College Students, 7e
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ChapterP: Preliminary Concepts
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The box-and-whisker plot shows the average temperatures in Orlando, Florida in January.

Which statement about the temperatures in Orlando must be true?

A. About half of the days in January had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.

C. The coldest day in January was 66 degrees.
D. The hottest day in December was 75 degrees.

### Box-and-Whisker Plot Explanation

A box-and-whisker plot, also known simply as a box plot, is a graphical representation used to display the distribution of a dataset. Here, we have a box-and-whisker plot with the following key components:

1. **Box**: The rectangular box represents the interquartile range (IQR) of the data, which contains the middle 50% of the data points. The left edge of the box marks the first quartile (Q1), and the right edge marks the third quartile (Q3).

2. **Median**: The vertical line inside the box indicates the median (Q2) of the dataset, which is the midpoint of the data.

3. **Whiskers**: The lines extending horizontally from the box are called whiskers. They represent the range of the data, excluding outliers. The left whisker extends from Q1 to the minimum value, while the right whisker extends from Q3 to the maximum value.

4. **Data Points**: Occasionally, the plot includes individual data points to indicate specific values, especially outliers, which are data points that fall significantly outside the expected range.

### Detailed Analysis

- **Minimum Value**: The leftmost point on the plot, which represents the minimum value, is at 51.
- **First Quartile (Q1)**: The left edge of the box, which represents the first quartile, is at 63.
- **Median (Q2)**: The vertical line inside the box, which represents the median, is at 69.
- **Third Quartile (Q3)**: The right edge of the box, which represents the third quartile, is at 72.
- **Maximum Value**: The rightmost point on the plot, which represents the maximum value, is at 84.

### Summary

This box-and-whisker plot provides a visual summary of the distribution of the dataset. It identifies key statistics such as the minimum, first quartile, median, third quartile, and maximum values, allowing for a quick and easy comparison of the spread and central tendency of the data.
Transcribed Image Text:### Box-and-Whisker Plot Explanation A box-and-whisker plot, also known simply as a box plot, is a graphical representation used to display the distribution of a dataset. Here, we have a box-and-whisker plot with the following key components: 1. **Box**: The rectangular box represents the interquartile range (IQR) of the data, which contains the middle 50% of the data points. The left edge of the box marks the first quartile (Q1), and the right edge marks the third quartile (Q3). 2. **Median**: The vertical line inside the box indicates the median (Q2) of the dataset, which is the midpoint of the data. 3. **Whiskers**: The lines extending horizontally from the box are called whiskers. They represent the range of the data, excluding outliers. The left whisker extends from Q1 to the minimum value, while the right whisker extends from Q3 to the maximum value. 4. **Data Points**: Occasionally, the plot includes individual data points to indicate specific values, especially outliers, which are data points that fall significantly outside the expected range. ### Detailed Analysis - **Minimum Value**: The leftmost point on the plot, which represents the minimum value, is at 51. - **First Quartile (Q1)**: The left edge of the box, which represents the first quartile, is at 63. - **Median (Q2)**: The vertical line inside the box, which represents the median, is at 69. - **Third Quartile (Q3)**: The right edge of the box, which represents the third quartile, is at 72. - **Maximum Value**: The rightmost point on the plot, which represents the maximum value, is at 84. ### Summary This box-and-whisker plot provides a visual summary of the distribution of the dataset. It identifies key statistics such as the minimum, first quartile, median, third quartile, and maximum values, allowing for a quick and easy comparison of the spread and central tendency of the data.
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