1. **Problem Statement:** Compare the three data sets (i), (ii), and (iii) based on their sample standard deviations and similarities/differences. 2. **Understanding Standard Deviation:** The sample standard deviation measures how spread out the data values are from the mean. A higher standard deviation means more variability. 3. **Analyzing Data Set (i):** It has two clusters of high frequency at values 4-5 and 9-10, which are far from the mean, indicating more spread. 4. **Analyzing Data Set (ii):** Frequencies are concentrated near the middle values 5-8, mostly around 6 and 7, indicating less spread and values close to the mean. 5. **Analyzing Data Set (iii):** Frequencies form a bell curve spread evenly from 4 to 10, showing moderate variability around the mean. 6. **Greatest Sample Standard Deviation:** Data set (i) has more entries farther from the mean, so it has the greatest sample standard deviation. 7. **Least Sample Standard Deviation:** Data set (ii) has more entries close to the mean, so it has the least sample standard deviation. 8. **Similarity and Differences:** All three data sets have the same range (3 to 11) and mean but differ in their standard deviations due to different spreads. **Final Answers:** - Greatest sample standard deviation: **B. Data set (i), because it has more entries that are farther away from the mean.** - Least sample standard deviation: **A. Data set (ii), because it has more entries that are close to the mean.** - How are the data sets the same/different: **D. The three data sets have the same range and mean but have different standard deviations.**