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The position for the 62nd percentile corresponds to the 73.16th data value in the ordered list. Since we cannot directly use a fractional index, we'll interpolate between the 73rd and 74th values.

Now, let's extract the 73rd and 74th values from the provided data and perform the interpolation.The 73rd value is 42.3, and the 74th value is 42.5. To find the 62nd percentile, we interpolate between these two values:

\[
P_{62} = 42.3 + 0.16 \times (42.5 - 42.3)
\]

Let me calculate that for you.The 62nd percentile (\( P_{62} \)) is approximately 42.32.

Would you like further details on how this was calculated, or any additional questions?

Here are some related questions to deepen your understanding:
1. How is the percentile formula derived for a data set?
2. What is the difference between interpolation and direct selection for percentiles?
3. How would you calculate the 25th or 75th percentile for this data set?
4. How does interpolation affect the result when the index is a decimal?
5. Why is it important to sort data before calculating percentiles?

**Tip:** Always sort the data before calculating percentiles to ensure accuracy.

As close as possible, identify the data value located at the 62nd percentile from a sorted dataset (n = 117).

Learn how to calculate the 62nd percentile from a dataset of 117 sorted values. We cover percentiles, interpolation, and the necessary formulas to find P_62, approximately 42.32.

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