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The image shows a set of ratings of men by women in an experiment involving speed dating. The task is to calculate the 5-number summary from these ratings and use it to construct a boxplot.

### The 5-number summary includes:
1. **Minimum value**: The smallest data point.
2. **First quartile (Q1)**: The 25th percentile.
3. **Median (Q2)**: The 50th percentile.
4. **Third quartile (Q3)**: The 75th percentile.
5. **Maximum value**: The largest data point.

### Let's calculate the 5-number summary:

The data given from the image is:
\[
1.0, 1.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 3.5, 4.0, 5.0, 5.5, 5.5, 5.5, 6.5, 6.5, 7.0, 8.0, 8.5
\]

#### Steps to calculate:
1. **Minimum**: 1.0
2. **Maximum**: 8.5
3. **Median (Q2)**: The middle value. Since there are 19 numbers, the 10th value is the median: 4.0
4. **Q1 (First Quartile)**: The median of the lower half of the data (the first 9 values): 
   - Lower half: \[1.0, 1.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 3.5\]
   - Median of the lower half (5th value): 3.0
5. **Q3 (Third Quartile)**: The median of the upper half of the data (the last 9 values): 
   - Upper half: \[4.0, 5.0, 5.5, 5.5, 5.5, 6.5, 6.5, 7.0, 8.0, 8.5\]
   - Median of the upper half (14th value): 5.5

### 5-Number Summary:
- Minimum: 1.0
- Q1: 3.0
- Median: 4.0
- Q3: 5.5
- Maximum: 8.5

Would you like more details or have any questions?

### Relative Questions:
1. How do you interpret each value in the 5-number summary?
2. What is the significance of quartiles in a dataset?
3. How does a boxplot visually represent the 5-number summary?
4. How would outliers affect the boxplot?
5. Can you calculate the interquartile range (IQR) from this data?

### Tip:
The interquartile range (IQR) is a useful measure of spread and can be found by subtracting Q1 from Q3.

The following are the ratings of men by women in an experiment involving speed dating. Use the given data to construct a boxplot and identify the 5-number summary.

Learn how to calculate a 5-number summary using data from a speed dating experiment. This step-by-step solution includes calculating the minimum, maximum, quartiles, and median. The problem is suitable for high school students in Grades 9-12.

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