Here is a sample data set (presented as a stem-&-leaf plot):
5.# | 6
6.# | 234479
7.# | 56
8.# | 48
9.# | 0378
10.# | 45

Construct a boxplot for data above without using any technology. Upload your work for full credits.

You can click and drag the points on the center of the box plot to change them.

To construct a boxplot from the given stem-and-leaf plot, let's follow the process step-by-step:

### 1. **Extract the dataTo construct a boxplot from the given stem-and-leaf plot, let's follow the process step-by-step:

### 1. **Extract the **
The stem-and-leaf plot provides the following dataTo construct a boxplot from the given stem-and-leaf plot, let's follow the process step-by-step:

### 1. **Extract the **
The stem-and-leaf plot provides the following 

- 5.# | 6 → 56
- 6.# | 234479 → 62, 63, 64, 64, 67, 69
- 7.# | 56 → 75, 76
- 8.# | 48 → 84, 88
- 9.# | 0378 → 90, 93, 97, 98
- 10.# | 45 → 104, 105

Now, list all the numbers:
\[ 56, 62, 63, 64, 64, 67, 69, 75, 76, 84, 88, 90, 93, 97, 98, 104, 105 \]

### 2. **Order the dataTo construct a boxplot from the given stem-and-leaf plot, let's follow the process step-by-step:

### 1. **Extract the **
The stem-and-leaf plot provides the following 

- 5.# | 6 → 56
- 6.# | 234479 → 62, 63, 64, 64, 67, 69
- 7.# | 56 → 75, 76
- 8.# | 48 → 84, 88
- 9.# | 0378 → 90, 93, 97, 98
- 10.# | 45 → 104, 105

Now, list all the numbers:
\[ 56, 62, 63, 64, 64, 67, 69, 75, 76, 84, 88, 90, 93, 97, 98, 104, 105 \]

### 2. **Order the **
The data is already ordered from least to greatest:
\[ 56, 62, 63, 64, 64, 67, 69, 75, 76, 84, 88, 90, 93, 97, 98, 104, 105 \]

### 3. **Find the five-number summary:**
- **Minimum** = 56
- **Q1** = First quartile (25th percentile): To calculate Q1, find the median of the lower half of the data (excluding the overall median). The lower half is:
  \[ 56, 62, 63, 64, 64, 67, 69, 75 \]
  Median of this set: \( \frac{64 + 64}{2} = 64 \)
  So, Q1 = 64.
  
- **Median** = The middle number of the entire data set. There are 17 values, so the middle one is the 9th number:
  Median = 76
  
- **Q3** = Third quartile (75th percentile): Find the median of the upper half:
  \[ 76, 84, 88, 90, 93, 97, 98, 104, 105 \]
  Median of this set: \( \frac{90 + 93}{2} = 91.5 \)
  So, Q3 = 91.5.
  
- **Maximum** = 105

### 4. **Draw the boxplot manually:**
Now, using the five-number summary:
- **Minimum** = 56
- **Q1** = 64
- **Median** = 76
- **Q3** = 91.5
- **Maximum** = 105

The box should span from Q1 to Q3 (64 to 91.5), with the median marked at 76. Whiskers extend to the minimum (56) and maximum (105).

Would you like a detailed explanation of any of the steps or further assistance? Here are five follow-up questions to explore this topic more:

1. How do you calculate quartiles for larger data sets?
2. What are potential outliers in a boxplot, and how do you detect them?
3. Can a boxplot be skewed? If yes, how do you determine the skewness?
4. What is the interquartile range (IQR) and its significance in data analysis?
5. How does a boxplot visually represent the spread and center of a data set?

**Tip:** Always ensure that your data is sorted when calculating quartiles for accurate results!

Here is a sample data set (presented as a stem-&-leaf plot):
5.# | 6
6.# | 234479
7.# | 56
8.# | 48
9.# | 0378
10.# | 45

Construct a boxplot for data above without using any technology. Upload your work for full credits.

Learn how to manually construct a boxplot from a stem-and-leaf plot. This problem involves extracting data, ordering it, and calculating the five-number summary, including minimum, Q1, median, Q3, and maximum values. Perfect for students in Grades 9-12.

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