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.