Using the following stem & leaf plot, find the five number summary for the data.

3 | 0 1 4 4 6 6 9 9
4 | 5 6 9
5 | 1 4 6 9 9
6 | 0 1 1 2 3 4 8 9 9
7 | 0 1 6 8 9
8 | 0 3 5 6 8 9
9 | 0 0 1 1 5 6 7 7 9 9 9


Five number summary:
 

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

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.

Using the following stem & leaf plot, find the five-number summary for the data.

3 | 0 1 4 4 6 6 9 9
4 | 5 6 9
5 | 1 4 6 9 9
6 | 0 1 1 2 3 4 8 9 9
7 | 0 1 6 8 9
8 | 0 3 5 6 8 9
9 | 0 0 1 1 5 6 7 7 9 9 9

Learn how to calculate the five-number summary from a stem-and-leaf plot with step-by-step explanations. This data set includes values from 30 to 99, providing a comprehensive look at descriptive statistics using the five-number summary (Min, Q1, Median, Q3, Max). Suitable for students in Grades 6-8.

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