https://file.aiquickdraw.com/mathbot/file/1726532967363ijx62znf.jpg

Let's analyze the data given in the image to construct the box-and-whisker plot step by step. Here are the temperatures of 22 cities in degrees Fahrenheit:

- 75, 48, 84, 77, 63, 67, 68, 81
- 79, 84, 35, 37, 77, 72, 65, 86
- 75, 69, 36, 88, 83, 68

### Step 1: Arrange the data in order
Ordered temperatures:
- 35, 36, 37, 48, 63, 65, 67, 68, 68, 69, 72, 75, 75, 77, 77, 79, 81, 83, 84, 84, 86, 88

### Step 2: Find the five-number summary
- **Minimum:** 35
- **Q1 (First Quartile):** The first quartile is the median of the lower half of the data (11 data points before the median).
  - Median of the lower half: (65 + 67) / 2 = 66
  - Q1 = 66
- **Median (Q2):** Median of the full dataset.
  - (72 + 75) / 2 = 73.5
  - Median = 73.5
- **Q3 (Third Quartile):** The third quartile is the median of the upper half (11 data points after the median).
  - Median of the upper half: (79 + 81) / 2 = 80
  - Q3 = 80
- **Maximum:** 88

### Step 3: Plot the box-and-whisker plot
- The "box" extends from Q1 (66) to Q3 (80), with the line at the median (73.5).
- The "whiskers" extend from the minimum (35) to the maximum (88).
- Any outliers, if there are any, are plotted individually. Here, there are no extreme outliers based on the interquartile range (IQR) criterion.

Now, you should be able to adjust the boxplot on your platform accordingly!

Would you like more details on how to handle outliers or how to calculate IQR?

### Related questions:
1. What is the interquartile range (IQR), and how is it calculated?
2. How do you identify outliers using the 1.5*IQR rule?
3. How do boxplots help in understanding the spread of the data?
4. What is the difference between Q1, Q2 (median), and Q3?
5. How do you interpret the whiskers in a boxplot?

**Tip:** When adjusting boxplots, ensure that your Q1, median, and Q3 are positioned correctly according to the five-number summary!

Below are the noontime temperatures (in degrees Fahrenheit) of 22 world cities measured on the same day. Construct a box-and-whisker plot (sometimes called a boxplot) by adjusting the given plot to plot outliers, if any.

Learn how to construct a box-and-whisker plot using temperature data from 22 world cities. The five-number summary and IQR help identify the spread and possible outliers. This guide is suitable for Grades 7-10 and covers key concepts in descriptive statistics.

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