1. **State the problem:** We have a data set of numbers and need to find the limits of the lowest cluster, the frequency of the lowest cluster, and the frequency of the fifth cluster. 2. **Organize the data:** Sort the data in ascending order: $$27, 48, 48, 48, 54, 57, 59, 59, 60, 61, 61, 62, 63, 64, 64, 65, 65, 66, 66, 67, 67, 67, 68, 68, 68, 68, 71, 71, 72, 72, 76, 76, 78, 80, 86, 94$$ 3. **Identify clusters:** Clusters are groups of numbers close to each other. We can group the data by similar values: - Cluster 1 (lowest): 27 - Cluster 2: 48, 48, 48, 54 - Cluster 3: 57, 59, 59, 60 - Cluster 4: 61, 61, 62, 63 - Cluster 5: 64, 64, 65, 65 - Cluster 6: 66, 66, 67, 67, 67 - Cluster 7: 68, 68, 68, 68 - Cluster 8: 71, 71, 72, 72 - Cluster 9: 76, 76, 78, 80 - Cluster 10: 86, 94 4. **Limits of the lowest cluster:** The lowest cluster is the first cluster with the value 27 only. So the limits are: - Lower limit: 27 - Upper limit: 27 5. **Frequency of the lowest cluster:** The frequency is the count of numbers in the cluster. For cluster 1, frequency = 1. 6. **Frequency of the fifth cluster:** The fifth cluster contains 64, 64, 65, 65. Frequency = 4. **Final answers:** - Limits of lowest cluster: 27 to 27 - Frequency of lowest cluster: 1 - Frequency of fifth cluster: 4