To calculate the 99th percentile for the given dataset, we can use the following steps:

### 1. **Rank the Data:**
The data arranged in ascending order is:

\[ 11, 28, 33, 39, 42, 43, 44, 47, 54, 71, 80, 86, 103, 104 \]

### 2. **Determine the Position for the 99th Percentile:**
The formula to find the position \(P\) for a given percentile \(k\) is:

\[
P = \frac{k}{100} \times (n + 1)
\]

Where:
- \(k\) is the desired percentile (99 in this case).
- \(n\) is the number of data points (14 in this case).

Substitute the values into the formula:

\[
P = \frac{99}{100} \times (14 + 1) = 0.99 \times 15 = 14.85
\]

### 3. **Interpret the Position:**
- Since the position 14.85 is between the 14th and 15th data points, we need to interpolate between these two points.
- The 14th data point is 104. Since there is no 15th data point (as we only have 14 values), the 99th percentile will be very close to the 14th data point.

### 4. **Estimate the 99th Percentile:**
- Given the position, the 99th percentile is approximately 104 (since it is close to the 14th value).

So, the 99th percentile for this dataset is approximately **104**.

Would you like to dive deeper into any specific part of this process or explore related concepts?

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Here are 5 related questions:

1. How would you calculate the 90th percentile for this dataset?
2. What does it mean when a data point lies above the 99th percentile?
3. How does the 99th percentile differ from the maximum value in a dataset?
4. How would the 99th percentile change if an outlier is added to the dataset?
5. What is the significance of the 50th percentile, and how is it related to the median?

**Tip:** The 99th percentile is often used in statistics to represent extreme values, which helps in understanding the tail behavior of a distribution.

Learn how to calculate the 99th percentile in a dataset using mathematical interpolation and percentile formulas. Understand the concept of percentiles and their application in statistics. Suitable for advanced high school students and anyone interested in statistical analysis.

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