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To calculate the 85th percentile for the given dataset, we follow these steps:

1. **Arrange the data in ascending order** (this step is unnecessary here, as the data is already sorted):
   \[
   11, 17.8, 18.9, 20.7, 45.8, 54.7, 56.1, 59.2, 60.2, 69.9
   \]

2. **Calculate the rank** corresponding to the 85th percentile using the formula:
   \[
   \text{Rank} = P \times (N + 1)
   \]
   Where:
   - \( P \) is the percentile (0.85 for the 85th percentile),
   - \( N \) is the number of data points.

   In this case, \( N = 10 \), so the rank is:
   \[
   \text{Rank} = 0.85 \times (10 + 1) = 0.85 \times 11 = 9.35
   \]

3. **Interpret the rank**:
   The rank 9.35 means that the 85th percentile lies between the 9th and 10th data points in the ordered list. 

4. **Interpolate between the 9th and 10th data points**:
   - The 9th data point is \( x_9 = 60.2 \),
   - The 10th data point is \( x_{10} = 69.9 \).

   To interpolate, we use the formula:
   \[
   \text{Percentile value} = x_9 + (x_{10} - x_9) \times (9.35 - 9)
   \]
   \[
   \text{Percentile value} = 60.2 + (69.9 - 60.2) \times 0.35
   \]
   \[
   \text{Percentile value} = 60.2 + 9.7 \times 0.35 = 60.2 + 3.395 = 63.595
   \]

So, the 85th percentile of the data is approximately **63.6**.

Would you like more details on the interpolation method or percentile calculations? 

Here are five questions to expand on this topic:
1. How are percentiles different from quartiles?
2. How does interpolation work in percentile calculations?
3. What are some applications of percentiles in real-world data analysis?
4. How would the method change if the data weren't already sorted?
5. How does the choice of formula affect percentile calculation methods?

**Tip:** When calculating percentiles, always make sure the data is sorted in ascending order before applying the percentile formula.

Calculate the 85th percentile of the data shown (11, 17.8, 18.9, 20.7, 45.8, 54.7, 56.1, 59.2, 60.2, 69.9).

Learn how to calculate the 85th percentile of a dataset with 10 values using the percentile rank formula and interpolation. The given data includes values from 11 to 69.9. Suitable for high school students (Grades 10-12).

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