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The study guide you've shared involves a few key tasks in elementary statistics. Here's a breakdown of what needs to be done:

1. **Construct a stem plot** for the given data.
2. **Find percentiles** \( P_{10} \), \( P_{50} \) (the 10th and 50th percentiles).
3. **Find the percentile ranking** for the value 30.

Let's start by tackling part (a), where we construct the **stem plot**.

The data provided consists of the ages of 32 randomly selected college students:
\[ 
23, 35, 32, 18, 19, 20, 40, 29, 24, 19, 23, 24, 50, 19, 32, 35, 42, 25, 28, 27, 20, 40, 45, 38, 40, 25, 30, 35, 30, 20 
\]

For a stem-and-leaf plot:
- The **stem** represents the tens digit.
- The **leaf** represents the units digit.

Let me create the stem plot for you now.Here is the stem-and-leaf plot based on the ages:

\[
\begin{array}{|c|c|}
\hline
\text{Stem (Tens)} & \text{Leaf (Units)} \\
\hline
1 & 8, 9, 9, 9 \\
2 & 0, 0, 0, 3, 3, 4, 4, 5, 5, 7, 8, 9 \\
3 & 0, 0, 2, 2, 5, 5, 5, 8 \\
4 & 0, 0, 0, 2, 5 \\
5 & 0 \\
\hline
\end{array}
\]

This completes part (a) of the study guide.

Shall we move on to parts (b) and (c) to find the percentiles \( P_{10} \) and \( P_{50} \)? Let me know if you need any details or have questions. 

Here are 5 questions you can explore further:
1. What is the process of constructing a stem-and-leaf plot?
2. How do you interpret the spread of data in a stem plot?
3. What are some advantages of using a stem-and-leaf plot?
4. How does a stem plot differ from a histogram?
5. How can we estimate the median using the stem plot?

**Tip:** Stem plots are useful for small datasets and allow easy visualization of the distribution of values.

Ages of 32 randomly selected college students are given. Tasks include constructing a stem plot, finding P10, finding P50, and determining the percentile ranking for the value 30.

This problem involves constructing a stem-and-leaf plot for the ages of 32 randomly selected college students, calculating the 10th and 50th percentiles (P10 and P50), and determining the percentile ranking for the value 30. Suitable for students in Grades 10-12 studying elementary statistics.

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