Let's analyze the data and solve the problem step by step as requested. ### **Given Information:** - 16 four-star films - 10 three-star films - 11 two-star films - 5 one-star films We need to create a frequency table with **relative frequency** and **cumulative frequency** for each rating. --- ## **Step 1: Calculate Frequency and Relative Frequency** First, let's list the frequency for each rating and find the total number of films. - **4 stars:** 16 films - **3 stars:** 10 films - **2 stars:** 11 films - **1 star:** 5 films **Total number of films = 16 + 10 + 11 + 5 = 42** **Relative frequency** is calculated as: \[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total}} \] Let's calculate it for each row, rounded to the nearest tenth of a percent: - **4 stars:** \( \frac{16}{42} \approx 0.381 \rightarrow 38.1\% \) - **3 stars:** \( \frac{10}{42} \approx 0.238 \rightarrow 23.8\% \) - **2 stars:** \( \frac{11}{42} \approx 0.262 \rightarrow 26.2\% \) - **1 star:** \( \frac{5}{42} \approx 0.119 \rightarrow 11.9\% \) **Explanation:** This step gives us the frequency and relative frequency for each rating. --- ## **Step 2: Calculate Cumulative Frequency** Cumulative frequency is found by adding each frequency from the top down. - **4 stars:** 16 (just the 4-star films) - **3 stars:** 16 + 10 = 26 - **2 stars:** 26 + 11 = 37 - **1 star:** 37 + 5 = 42 **Explanation:** This step shows the running total of the number of films as we move down the ratings. --- ## **Final Answer: Frequency Table** | Stars | Frequency | Relative Frequency | Cumulative Frequency | |-------|-----------|-------------------|---------------------| | 4 | 16 | 38.1% | 16 | | 3 | 10 | 23.8% | 26 | | 2 | 11 | 26.2% | 37 | | 1 | 5 | 11.9% | 42 | | **Total** | **42** | **100%** | | --- **Final Explanation:** - **Step 1:** Found the frequency, total, and relative frequency for each rating. - **Step 2:** Added cumulative frequency for each rating. - The completed table summarizes all the required information.