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The image you provided contains a mathematical exercise about **percentiles**. Let's go through an assessment of the solution presented.

### Problem Overview
The task is to find the **20th percentile** for the given dataset:  
\[ 18, 20, 21, 23, 27, 35, 51, 55, 28 \]  
The exercise involves using a formula to calculate percentiles:

#### Formula:
\[
P_k = \frac{k}{100}(n+1)
\]
Where:
- \(P_k\) is the position of the \(k\)-th percentile,
- \(k\) is the desired percentile (in this case, 20th percentile),
- \(n\) is the number of data points.

### Steps Taken in the Solution:
1. **Order the Data**:  
   The data should be arranged in ascending order. The ordered dataset is:
   \[
   18, 20, 21, 23, 27, 28, 35, 51, 55
   \]
   This is correctly noted.

2. **Calculate \(P_{20}\)**:  
   Using the formula for the 20th percentile:
   \[
   P_{20} = \frac{20}{100} \times (9 + 1) = \frac{20}{100} \times 10 = 2
   \]
   This is the 2nd position in the ordered dataset.

3. **Locate the 20th Percentile**:  
   The 2nd value in the ordered dataset is 20, so the 20th percentile is **20**.

4. **Interpretation**:  
   The solution interprets that 20% of teachers in the CES dataset are 20 years old or younger, while 80% are older.

### Assessment of the Work:
- **Correctness**: The solution is accurate in both the formula application and the data ordering. The final percentile calculation and its interpretation are correct.
  
- **Presentation**: The steps are clearly organized with proper use of the formula, and the interpretation is straightforward.

- **Improvements**: 
  - It could be beneficial to provide a more general explanation of percentiles for clarity.
  - The formula could include some context for why the "n+1" adjustment is used (though it is standard in percentile calculations).
  
Overall, the solution is complete and correctly solves the problem.

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Would you like any additional details or explanations? Here are 5 follow-up questions to further explore the concept:

1. How would the calculation change if we wanted to find the 90th percentile?
2. Can you explain why we add 1 to the number of data points in the formula?
3. How would the interpretation change if the dataset were about ages in a different context, such as students?
4. What does it mean if a data point lies in the 50th percentile?
5. How would we estimate a percentile if the result of \(P_k\) was not a whole number?

**Tip**: When working with percentiles, always ensure your data is ordered properly, as the entire process relies on the relative positioning of values!

Given the following data set of the ages of teachers in CES: 18, 20, 21, 23, 27, 28, 35, 51, 55. Find the 20th percentile.

Learn how to calculate the 20th percentile for a data set representing the ages of teachers in CES. This problem covers essential statistical concepts such as percentiles, data ordering, and using the percentile position formula. Suitable for students in Grades 9-12.

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