1. **Problem Statement:** We are given two sets of service times for customers at two outlets: Thika Road (60 data points) and Mombasa Road (50 data points). Our tasks: - a) Construct stem-and-leaf diagrams for both outlets. - b) i) Compare the service times and draw conclusions. ii) Identify the mode (most frequent service time) for each outlet. - c) Construct grouped frequency distributions for both outlets. 2. **a) Construct Stem-and-Leaf Diagrams:** **Stem-and-leaf diagram separates each data point into a 'stem' (all but last digit) and a 'leaf' (last digit).** Here, because data mostly range from 10 to 65, stem = tens, leaf = units. **For Thika Road (x):** Group data by tens: - Stem 1 (10-19): Leaves are from data such as 10,12,15,... Leaves: 0,0,2,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9 (Order leaves ascending) - Stem 2 (20-29): Leaves from 20,21,22,... Leaves: 0,1,1,1,2,2,2,3,4,4,5,5 - Stem 3 (30-39): Leaves from 30,31,32,... Leaves: 0,0,1,2,2,3,5 - Stem 4 (40-49): Leaves 0,0,1,5,5 - Stem 5 (50-59): Leaves 0,0,1,2,2,3,5,5 - Stem 6 (60-69): Leaves 1,2,3,5,5,5,5 **Simplified and ordered Thika Road stem-and-leaf:** 1 | 0 0 2 2 2 3 3 4 4 5 5 6 6 7 7 8 8 2 | 0 1 1 1 2 2 2 3 4 4 5 5 3 | 0 0 1 2 2 3 5 4 | 0 0 1 5 5 5 | 0 0 1 2 2 3 5 5 6 | 1 2 3 5 5 5 5 **For Mombasa Road (y):** Group similarly: 1 | 0 0 0 1 2 2 5 5 2 | 0 0 2 3 5 5 5 5 3 | 0 0 2 3 5 5 4 | 0 0 5 5 6 8 5 | 0 1 2 5 5 5 5 5 5 6 6 | 0 0 5 3. **b i) Comparison and Conclusion:** - Thika Road has a wider spread and higher maximum times (up to 65). - Mombasa Road times cluster more between 10 to 55, indicating quicker service more consistently. - Therefore, Mombasa Road generally has lower and more consistent service times. 3. **b ii) Mode (Most Frequent Time):** - Thika Road: Times that appear most frequently are 65 (three times) and several others appear twice. - Mombasa Road: 55 appears very frequently (multiple occurrences). 4. **c) Grouped Frequency Distribution Tables:** Using class intervals of width 10: | Class Interval | Thika Frequency | Mombasa Frequency | |----------------|-----------------|------------------| | 10 - 19 | 18 | 10 | | 20 - 29 | 12 | 8 | | 30 - 39 | 7 | 6 | | 40 - 49 | 5 | 6 | | 50 - 59 | 8 | 14 | | 60 - 69 | 10 | 6 | **Final summary:** Stem-and-leaf plots provide a visual distribution. Mombasa Road shows generally shorter and more consistent wait times. Thika Road has longer and more varied times. Modes indicate that Mombasa Road's most common is 55, Thika Road's most common is 65. q_count = 3