
  Construct a box-and-whisker plot for these data (sample of 12) .   
 35  29  44  72  34  64  41  50  54  104  39  58 

To construct a box-and-whisker plot (also known as a box plot) for this data sample of 12 values, follow these steps:

### Data Set:
\[ 35, 29, 44, 72, 34, 64, 41, 50, 54, 104, 39, 58 \]

### Steps:

1. **Sort the data in ascending order:**
   \[ 29, 34, 35, 39, 41, 44, 50, 54, 58, 64, 72, 104 \]

2. **Find the minimum and maximum values (whiskers):**
   - **Minimum (Q0)** = 29
   - **Maximum (Q4)** = 104

3. **Determine the quartiles:**
   - **First Quartile (Q1)**: The median of the lower half of the data (excluding the median itself if the dataset is odd).
   - **Second Quartile (Q2 or Median)**: The median of the entire dataset.
   - **Third Quartile (Q3)**: The median of the upper half of the data (excluding the median itself if the dataset is odd).

   - Lower half: \[ 29, 34, 35, 39, 41, 44 \]
     - Median (Q1) = \(\frac{35 + 39}{2} = 37\)

   - Upper half: \[ 50, 54, 58, 64, 72, 104 \]
     - Median (Q3) = \(\frac{58 + 64}{2} = 61\)

4. **Calculate the median (Q2):**
   - The median (middle of the entire data set): \(\frac{44 + 50}{2} = 47\)

### Five-Number Summary:
- **Minimum** = 29
- **Q1** = 37
- **Median (Q2)** = 47
- **Q3** = 61
- **Maximum** = 104

### Box-and-Whisker Plot Components:
- The "box" extends from Q1 (37) to Q3 (61).
- The "whiskers" extend from the minimum value (29) to the maximum value (104).
- The median (47) is represented by a line inside the box.

Would you like further explanation on how to interpret the box-and-whisker plot?

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**Relative Questions:**
1. How do you interpret outliers in a box-and-whisker plot?
2. What does the interquartile range (IQR) tell us in this dataset?
3. How do whiskers in the box plot relate to variability?
4. Can a box plot show skewness in a dataset?
5. How would the box plot change if the dataset had more extreme values?

**Tip**: Box-and-whisker plots are great for visualizing data distribution, especially the spread and potential outliers.

Construct a box-and-whisker plot for these data (sample of 12) . 35  29  44  72  34  64  41  50  54  104  39  58

Learn how to construct a box-and-whisker plot for a sample of 12 data points: 35, 29, 44, 72, 34, 64, 41, 50, 54, 104, 39, 58. This problem covers core statistical concepts, including quartiles and five-number summaries, making it suitable for students in Grades 8-10.

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