Using the following stem \& leaf plot, find the five number summary for the data by hand. 1123 \( 2 \mid 234 \) \( 3 \mid 23 \) \( 4 \mid 4588 \) 5112344 \( 6 \mid 01 \) Min \( =12 \) \( 0^{6} \) Q1 \( =23 \) Med \( =45 \) Q3 \( =53 \) \( 0^{6} \) Max \( =61 \) \( O^{6} \)

To determine the **five-number summary** from the given **stem-and-leaf plot**, we'll follow these steps: 1. **Understand the Stem-and-Leaf Plot:** The provided stem-and-leaf plot appears as follows: ``` 1 | 1 2 3 2 | 2 3 4 3 | 2 3 4 | 4 5 8 8 5 | 1 1 2 3 4 4 6 | 0 1 ``` Here, the **stem** represents the **tens place**, and the **leaves** represent the **units place**. For example, the stem `2 | 2 3 4` corresponds to the numbers **22, 23, 24**. 2. **List All Data Points in Order:** Extracting all the data points from the stem-and-leaf plot: ``` 11, 12, 13, 22, 23, 24, 32, 33, 44, 45, 48, 48, 51, 51, 52, 53, 54, 54, 60, 61 ``` **Total Data Points (N):** 20 3. **Identify the Five-Number Summary Components:** The five-number summary consists of: - **Minimum (Min):** The smallest data point. - **First Quartile (Q1):** The median of the lower half of the data. - **Median:** The middle value of the data. - **Third Quartile (Q3):** The median of the upper half of the data. - **Maximum (Max):** The largest data point. 4. **Calculate Each Component:** - **Minimum (Min):** The smallest number in the dataset is **11**. - **Maximum (Max):** The largest number in the dataset is **61**. - **Median:** - Since there are **20** data points (an even number), the median is the average of the 10th and 11th values. - 10th value: **45** - 11th value: **48** - **Median = (45 + 48) / 2 = 46.5** - **First Quartile (Q1):** - Q1 is the median of the first half of the data (first 10 numbers). - First 10 numbers: **11, 12, 13, 22, 23, 24, 32, 33, 44, 45** - The median of these is the average of the 5th and 6th values: **23** and **24**. - **Q1 = (23 + 24) / 2 = 23.5** - **Third Quartile (Q3):** - Q3 is the median of the second half of the data (last 10 numbers). - Last 10 numbers: **48, 48, 51, 51, 52, 53, 54, 54, 60, 61** - The median of these is the average of the 5th and 6th values: **52** and **53**. - **Q3 = (52 + 53) / 2 = 52.5** 5. **Final Five-Number Summary:** Based on the calculations: - **Minimum (Min):** 11 - **First Quartile (Q1):** 23.5 - **Median:** 46.5 - **Third Quartile (Q3):** 52.5 - **Maximum (Max):** 61 ``` Five-Number Summary: Min = 11 Q1 = 23.5 Median = 46.5 Q3 = 52.5 Max = 61 ``` **Note:** The values provided by you (Min = 12, Q1 = 23, Median = 45, Q3 = 53, Max = 61) are slightly different from the calculated ones. This discrepancy might be due to different interpretations of the stem-and-leaf plot or rounding conventions. Ensure that all data points are correctly extracted and that the quartiles are calculated using the appropriate method based on the dataset size.