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Let's analyze the data set to calculate the 25th, 50th, and 75th percentiles.

Here is the given list of dataLet's analyze the data set to calculate the 25th, 50th, and 75th percentiles.

Here is the given list of 

```
2, 3, 4, 7, 8, 13, 14, 16, 18, 19, 20, 28, 32, 35, 37, 41,
46, 48, 50, 53, 55, 58, 60, 64, 65, 69, 74, 75, 78, 81, 84, 97
```

### Step 1: Sort the data (which is already sorted).

The dataset contains 32 data points.

### Step 2: Percentile Calculation

- **25th percentile (Q1)**: The formula to find the percentile position is:

  \[
  P_k = \frac{k(n+1)}{100}
  \]
  where \( P_k \) is the position of the \( k \)-th percentile, and \( n \) is the number of data points.

  For the 25th percentile (k = 25):
  \[
  P_{25} = \frac{25(32+1)}{100} = \frac{825}{100} = 8.25
  \]
  The 8th position (rounded to the nearest whole number) corresponds to **18**.

- **50th percentile (Q2 or Median)**: This corresponds to the median. For an even number of data points, the median is the average of the 16th and 17th numbers:

  \[
  Median = \frac{41 + 46}{2} = \frac{87}{2} = 43.5
  \]

- **75th percentile (Q3)**: For the 75th percentile (k = 75):
  \[
  P_{75} = \frac{75(32+1)}{100} = \frac{2475}{100} = 24.75
  \]
  The 25th position corresponds to **65**.

### Final Values:
- **25th percentile** = 18
- **50th percentile (Median)** = 43.5
- **75th percentile** = 65

Would you like further details on the steps or clarification on how these values were determined?

Here are five related questions to explore this concept:
1. How would you calculate the 90th percentile for this data set?
2. What is the interquartile range (IQR) of this data set?
3. How does the formula for percentiles change if there are outliers in the data set?
4. How can quartiles help in identifying skewness in data distribution?
5. What are the differences between percentiles and quartiles?

**Tip:** Always ensure that your data is sorted before calculating percentiles, as the calculations rely on the position within the ordered set.

Find the 25th, 50th, and 75th percentiles from the following list of 32 data points.

Learn how to calculate the 25th, 50th, and 75th percentiles from a list of 32 data points using statistical formulas. This problem covers key statistical concepts and percentile calculation, suitable for high school students.

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