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To find the 94th percentile (\( P_{94} \)) from the given data, we need to follow these steps:

1. **Organize the data in ascending order** (which it already is).
2. **Find the total number of data points (n):**
   In the provided table, there are 6 rows and 6 columns, making a total of \( 6 \times 6 = 36 \) data points.
   
3. **Determine the position of the 94th percentile** using the formula:
   \[
   P_k = \frac{k}{100} \times (n + 1)
   \]
   where \( k = 94 \) and \( n = 36 \).

4. **Calculate the position:**
   \[
   P_{94} = \frac{94}{100} \times (36 + 1) = 0.94 \times 37 = 34.78
   \]

   This means that the 94th percentile lies between the 34th and 35th data points.

5. **Identify the values at these positions:**
   - The 34th value is **840**.
   - The 35th value is **860**.

6. **Interpolate to find \( P_{94} \):**
   Since \( P_{94} \) is at position 34.78, we can interpolate between 840 and 860:
   \[
   P_{94} = 840 + (860 - 840) \times (34.78 - 34)
   \]
   \[
   P_{94} = 840 + 20 \times 0.78 = 840 + 15.6 = 855.6
   \]

Thus, the 94th percentile is approximately **855.6**.

Would you like further clarification or details? Here are five related questions to expand your understanding:

1. What is the formula for calculating percentiles in a data set?
2. How do you interpolate between two data points for non-integer percentiles?
3. What is the difference between percentiles and quartiles?
4. Can the 50th percentile be considered the median?
5. How does increasing the data set size affect the position of percentiles?

**Tip:** When calculating percentiles, always ensure the data is ordered correctly, as this directly impacts the results.

Find the 94th percentile (P94) from the given data set of 36 values arranged in ascending order.

Learn how to calculate the 94th percentile from a data set of 36 values using percentile and interpolation formulas. This guide walks through step-by-step instructions to determine the percentile position and perform interpolation between data points.

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