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.

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!