Below are 36 sorted ages of an acting award winner. Find Upper P 60 using the method presented in the textbook.
17
17
18
22
22
24
30
31
31
31

34
34
39
43
43
43
45
47
49
49
50
57
57
59
61
62
62
64
64
65
66
70
71
74
76
79

To find the **Upper P60** (the 60th percentile) from the given list of 36 sorted ages, follow these steps:

### Step 1: Calculate the position of the 60th percentile.
The formula to find the position (rank) of a percentile in a sorted data set is:

\[
P_n = \frac{n}{100} \times (N + 1)
\]

Where:
- \( P_n \) is the position of the nth percentile.
- \( n \) is the desired percentile (in this case, 60).
- \( N \) is the total number of data points (in this case, 36).

So for the 60th percentile:

\[
P_{60} = \frac{60}{100} \times (36 + 1) = 0.60 \times 37 = 22.2
\]

### Step 2: Interpolate to find the value at this position.
Since \( P_{60} = 22.2 \), this means the 60th percentile lies between the 22nd and 23rd values in the sorted data.

From the sorted list of ages:
- The 22nd value is **57**.
- The 23rd value is **57**.

Since the 60th percentile falls between the two identical values, **the Upper P60 is 57**.

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Would you like further details or clarification on any part of this process?

Here are 5 related questions you might explore:
1. How would the process change if the list had an odd number of values?
2. Can you explain how interpolation works when the values are not the same?
3. What is the 75th percentile in this same data set?
4. How does the 60th percentile relate to the median (50th percentile)?
5. How is the percentile different from a quartile?

**Tip:** When dealing with percentiles, always remember to sort the data before applying any formulas!

Below are 36 sorted ages of an acting award winner. Find Upper P 60 using the method presented in the textbook.

Learn how to calculate the 60th percentile (Upper P60) for a sorted data set of 36 ages, using the percentile formula and interpolation method. This example uses acting award winners' ages and is suitable for high school students, covering key concepts in data analysis and percentiles.

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