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Lesson: 3.3 Measures of Relative PositionROBIN HAVEN  

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 2 of 3 :  Find the first quartile.

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To find the first quartile (Q1), we follow a similar process to finding the second quartile but focus on the lower 25% of the data.

### Step 1: List the Data
As we did before, the ordered list of commute times 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 Q1
- The first quartile (Q1) is the median of the lower half of the data.
- Since there are 26 data points, the lower half consists of the first 13 data points.
- The position of Q1 is at:
  \[
  \text{Position} = \frac{n+1}{4} = \frac{26+1}{4} = \frac{27}{4} = 6.75
  \]
- Q1 will be the average of the 6th and 7th data points in the ordered list.

### Step 3: Find Q1
- The 6th data point is 16, and the 7th data point is 19.
- So, the first quartile (Q1) is:
  \[
  Q1 = \frac{16 + 19}{2} = \frac{35}{2} = 17.5
  \]

**Answer**: The first quartile (Q1) is 17.5 minutes.

Would you like to continue with finding the third quartile (Q3) or have any other questions? Here are some related queries:

1. How do you find the third quartile (Q3) for this data?
2. How can the quartiles be used to calculate the interquartile range (IQR)?
3. What is the significance of Q1 in understanding the data distribution?
4. How can quartiles help identify potential outliers?
5. What is the difference between quartiles and percentiles?

**Tip**: The first quartile (Q1) helps you understand where the lower 25% of your data lies, providing insight into the distribution's spread.

Learn how to find quartiles from commute time data using a stem-and-leaf plot. This step-by-step guide covers the process of calculating the first quartile (Q1) for given commute times in minutes, providing insights into data distribution and statistical analysis. Suitable for high school students and anyone interested in data analysis.

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