(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.