The stem-and-leaf plot provided shows hexachlorobenzene concentrations in micrograms per liter from 9 workers' uniforms. Here are the values extracted from the plot:

• 0 | 4 → 0.04
• 0 | 6 → 0.06
• 0 | 6 → 0.06
• 0 | 7 → 0.07
• 0 | 9 → 0.09
• 1 | 1 → 0.11
• 1 | 3 → 0.13
• 1 | 4 → 0.14
• 2 | 3 → 0.23

Step 1: Arrange the data in ascending order:

0.04, 0.06, 0.06, 0.07, 0.09, 0.11, 0.13, 0.14, 0.23

Step 2: Find the quartiles

• Q1 (First quartile): The first quartile is the median of the lower half of the data. The lower half consists of the first 4 values: 0.04, 0.06, 0.06, and 0.07. The median of this group is between 0.06 and 0.06, so Q1 = 0.06.

• Q2 (Median): The median of the entire data set is the middle value. There are 9 values, so the median is the 5th value, which is Q2 = 0.09.

• Q3 (Third quartile): The third quartile is the median of the upper half of the data. The upper half consists of the last 4 values: 0.11, 0.13, 0.14, and 0.23. The median of this group is between 0.13 and 0.14, so Q3 = 0.135.

Step 3: Calculate the interquartile range (IQR)

The interquartile range is given by: $\text{IQR} = Q3 - Q1 = 0.135 - 0.06 = 0.075$

Thus, the interquartile range (IQR) is 0.075 micrograms per liter.

Would you like more details or have any questions?

Follow-up Questions:

1. How would you interpret the interquartile range in a real-world context for this data?
2. What does the median concentration of 0.09 tell us about the central tendency of the data?
3. How does the stem-and-leaf plot compare to other ways of representing data, such as histograms or box plots?
4. What might a high or low IQR indicate about the variability of the chemical concentrations on workers' uniforms?
5. Could outliers affect the IQR, and how would you detect them in this data set?

Tip: When interpreting stem-and-leaf plots, remember that they provide both the shape and distribution of data, making it easy to find median and quartiles.