https://file.aiquickdraw.com/mathbot/file/1725461453104gzh9vq09.jpg

To calculate the 72nd percentile from the data, let's follow these steps:

1. **Organize the Data**: Ensure the data is ordered from smallest to largest (if not already).
2. **Find the Rank**: Use the formula for the rank (position in the data) of the percentile:
   \[
   \text{Rank} = \frac{P}{100} \times (N + 1)
   \]
   where \( P \) is the percentile (72 in this case) and \( N \) is the number of data points.
3. **Interpolate if Necessary**: If the rank is not an integer, interpolate between the two closest data points.

Let me analyze the specific data and calculations shown in your image.

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After analyzing the image, here are the steps applied:

- The percentile being asked is the 72nd percentile.
- The number of data points (N) is not explicitly listed in the image, but the calculations hint at \( N = 10 \), which is typically used in percentile calculations in a table format like the one shown.
- The rank can be calculated as follows:

  \[
  \text{Rank} = \frac{72}{100} \times (10 + 1) = 0.72 \times 11 = 7.92
  \]

  This means the 72nd percentile lies between the 7th and 8th data points.

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The specific data points around this rank were:
- \( x_7 = 75 \)
- \( x_8 = 75 \)

Since these two points are equal, interpolation results in 75 for the 72nd percentile.

### The 72nd percentile is **75**.

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Would you like more details on the process or have any other questions?

Here are 5 follow-up questions:
1. How do you calculate the percentile if the rank is an integer?
2. Can you find the 90th percentile using the same data?
3. What does the percentile tell you about the data distribution?
4. How would you calculate a percentile if the data has outliers?
5. How would the calculation change if you had a larger data set?

**Tip:** When calculating percentiles, always ensure your data is sorted in ascending order to avoid incorrect calculations.

Learn how to calculate the 72nd percentile using the formula Rank = (P / 100) * (N + 1). In this example, the data is analyzed to find that the 72nd percentile corresponds to the value 75.

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