
The following stem-and-leaf plot represents the times in minutes required for 26
 co-workers to commute to work. Use the data provided to find the quartiles.

Commute Times in Minutes
Stem	Leaves
1
0
4
4
6
6
6
9
2
2
4
4
5
8
3
3
4
4
5
6
8
4
0
0
3
3
5
6
7
8
Key:  1|0=10

Step 1 of 3 :  Find the second quartile.
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To find the second quartile (Q2), which is also known as the median, we need to follow these steps:

1. **List the data**: Convert the stem-and-leaf plot into an ordered list of commute times.
2. **Determine the position of Q2**: Since Q2 is the median, it will be at the \(\frac{n+1}{2}\) position, where \(n\) is the total number of data points.
3. **Find Q2**: Identify the value corresponding to this position.

### Step 1: List the Data
Let's convert the stem-and-leaf plot into an ordered list of the 26 commute times:

- **Stem 1:** 10, 14, 14, 16, 16, 16, 19
- **Stem 2:** 22, 24, 24, 25, 28
- **Stem 3:** 33, 34, 34, 35, 36, 38
- **Stem 4:** 40, 40, 43, 43, 45, 46, 47, 48

So, the ordered data set is:
\[ 10, 14, 14, 16, 16, 16, 19, 22, 24, 24, 25, 28, 33, 34, 34, 35, 36, 38, 40, 40, 43, 43, 45, 46, 47, 48 \]

### Step 2: Determine the Position of Q2
- Total number of data points, \(n = 26\).
- The position of the median (Q2) is at:
  \[
  \text{Position} = \frac{n+1}{2} = \frac{26+1}{2} = \frac{27}{2} = 13.5
  \]

### Step 3: Find Q2
- Since the position is 13.5, Q2 will be the average of the 13th and 14th data points in the ordered list.
- The 13th data point is 33, and the 14th data point is 34.

So, the second quartile (Q2) is:
\[
Q2 = \frac{33 + 34}{2} = \frac{67}{2} = 33.5
\]

**Answer**: The second quartile (Q2) is 33.5 minutes.

Would you like to calculate the other quartiles or have more details? Here are some additional questions:

1. How do you find the first quartile (Q1) from this data?
2. What is the third quartile (Q3) of the dataset?
3. How do you calculate the interquartile range (IQR)?
4. Can you identify any outliers based on the IQR?
5. How does a stem-and-leaf plot help in understanding data distribution?

**Tip**: The median divides your data into two equal halves, making it a great measure of central tendency for skewed distributions.

Learn how to find quartiles from a stem-and-leaf plot using a step-by-step guide. This problem involves understanding descriptive statistics and quartile calculation from given commute times. Suitable for high school students and learners of statistics.

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