1. **State the problem:** We are given a set of ratings and need to find the 5-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. 2. **List the data in ascending order:** $$1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.5, 2.5, 2.5, 2.5, 2.5, 3.0, 3.5, 3.5, 3.5, 3.5, 4.5, 4.5, 5.5, 6.0$$ 3. **Identify the minimum and maximum:** - Minimum = $1.0$ - Maximum = $6.0$ 4. **Find the median (Q2):** - There are 20 data points (even number). - Median is the average of the 10th and 11th values. - 10th value = $2.5$, 11th value = $2.5$ - Median = $$\frac{2.5 + 2.5}{2} = 2.5$$ 5. **Find the first quartile (Q1):** - Q1 is the median of the lower half (first 10 values): $$1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.5, 2.5, 2.5, 2.5$$ - Median of these 10 values is average of 5th and 6th values: both $2.0$ - $$Q1 = \frac{2.0 + 2.0}{2} = 2.0$$ 6. **Find the third quartile (Q3):** - Q3 is the median of the upper half (last 10 values): $$2.5, 3.0, 3.5, 3.5, 3.5, 3.5, 4.5, 4.5, 5.5, 6.0$$ - Median is average of 5th and 6th values: both $3.5$ - $$Q3 = \frac{3.5 + 3.5}{2} = 3.5$$ 7. **Summary:** - Minimum = $1.0$ - Q1 = $2.0$ - Median = $2.5$ - Q3 = $3.5$ - Maximum = $6.0$ 8. **Answer to fill in the blanks:** The 5-number summary is $1.0$, $2.0$, $2.5$, $3.5$, and $6.0$. This completes the 5-number summary needed for the boxplot.