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use the box-and-whisker plot to
identify (a) the five-number summary, and (b) the interquartile range.

### (a) Five-Number Summary:

The five-number summary of a data set consists of the following:

1. **Minimum (Smallest value):** \(-1.9\)
2. **First Quartile (Q1):** \(-0.5\)
3. **Median (Q2):** \(0.1\)
4. **Third Quartile (Q3):** \(0.7\)
5. **Maximum (Largest value):** \(2.1\)

So, the five-number summary is:
\[
\text{Minimum: } -1.9, \quad Q1: -0.5, \quad Q2 (\text{Median}): 0.1, \quad Q3: 0.7, \quad \text{Maximum: } 2.1
\]

### (b) Interquartile Range (IQR):

The interquartile range is calculated as the difference between the third quartile (Q3) and the first quartile (Q1):
\[
\text{IQR} = Q3 - Q1 = 0.7 - (-0.5) = 0.7 + 0.5 = 1.2
\]

So, the Interquartile Range (IQR) is \(1.2\).

Would you like any further details or explanations on this topic?

### Related Questions:
1. How is the median of a data set determined from a box plot?
2. What does the interquartile range tell us about the spread of data?
3. What are outliers and how can they be identified using a box plot?
4. How do you interpret a skewed box plot?
5. What is the significance of the whiskers in a box-and-whisker plot?
6. Can the box plot be used to detect symmetry in a data set?
7. What is the relationship between the quartiles and percentiles in a data set?
8. How does the range of a data set differ from the interquartile range?

### Tip:
The interquartile range (IQR) is a robust measure of variability that is less affected by outliers compared to the full range.

Learn how to use a box-and-whisker plot to identify the five-number summary and interquartile range of a dataset. This problem covers key statistical concepts including quartiles, median, minimum, maximum, and interquartile range. Suitable for students in Grades 9-12.

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