To find the five-number summary (minimum, Q1, median, Q3, and maximum) for the data represented by the stem and leaf plot, let's first extract and list all the data points in order:

Data Extraction from the Stem-and-Leaf Plot:

• 3 | 0 1 4 4 6 6 9 9: 30, 31, 34, 34, 36, 36, 39, 39
• 4 | 5 6 9: 45, 46, 49
• 5 | 1 4 6 9 9: 51, 54, 56, 59, 59
• 6 | 0 1 1 2 3 4 8 9 9: 60, 61, 61, 62, 63, 64, 68, 69, 69
• 7 | 0 1 6 8 9: 70, 71, 76, 78, 79
• 8 | 0 3 5 6 8 9: 80, 83, 85, 86, 88, 89
• 9 | 0 0 1 1 5 6 7 7 9 9 9: 90, 90, 91, 91, 95, 96, 97, 97, 99, 99, 99

Ordered Data:

30, 31, 34, 34, 36, 36, 39, 39, 45, 46, 49, 51, 54, 56, 59, 59, 60, 61, 61, 62, 63, 64, 68, 69, 69, 70, 71, 76, 78, 79, 80, 83, 85, 86, 88, 89, 90, 90, 91, 91, 95, 96, 97, 97, 99, 99, 99

Five-Number Summary Calculation:

1. Minimum (Min): The smallest number in the dataset is 30.
2. First Quartile (Q1): This is the median of the lower half of the data (excluding the overall median if the data count is odd).
   • The lower half of the data is: 30, 31, 34, 34, 36, 36, 39, 39, 45, 46, 49, 51, 54, 56, 59, 59, 60, 61, 61, 62, 63, 64
   • There are 23 data points, so Q1 is the 12th value: 49.
3. Median (Q2): This is the middle value of the dataset.
   • There are 47 values, so the median is the 24th value: 69.
4. Third Quartile (Q3): This is the median of the upper half of the data (excluding the overall median if the data count is odd).
   • The upper half of the data is: 69, 70, 71, 76, 78, 79, 80, 83, 85, 86, 88, 89, 90, 90, 91, 91, 95, 96, 97, 97, 99, 99, 99
   • There are 23 data points, so Q3 is the 36th value: 89.
5. Maximum (Max): The largest number in the dataset is 99.

Final Five-Number Summary:

• Minimum (Min): 30
• First Quartile (Q1): 49
• Median (Q2): 69
• Third Quartile (Q3): 89
• Maximum (Max): 99

Would you like a detailed explanation of how these values were found or have any questions?

Relative Questions:

1. How can the five-number summary be used to identify outliers?
2. What is the significance of the interquartile range (IQR) in a five-number summary?
3. How can stem-and-leaf plots help in understanding the distribution of data?
4. How do you calculate the mean from a stem-and-leaf plot?
5. What are the differences between a stem-and-leaf plot and a box plot in representing data?

Tip:

Always double-check the data extracted from the stem-and-leaf plot to ensure accuracy before calculating statistical measures.