https://file.aiquickdraw.com/mathbot/file/1727027137520jpdy0lne.jpg

To solve this, the problem asks for the **upper fence** of a dataset, which is used as the **cutoff point**. The upper fence is a common method for detecting outliers, typically defined as:

\[
\text{Upper Fence} = Q3 + 1.5 \times IQR
\]

Where:
- \( Q3 \) is the third quartile (75th percentile),
- \( IQR \) is the interquartile range (the difference between \( Q3 \) and \( Q1 \), the first quartile).

Let's first extract the data from the image and calculate the quartiles, IQR, and finally the upper fence.

### The data provided:
\[
\{ 304, 494, 326, 401, 303, 336, 365, 374, 383, 386, 328, 392, 379, 514, 360, 509, 456, 358, 334, 478 \}
\]

I will now calculate the upper fence.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you want to continue, you could try solving this manually by calculating the quartiles (Q1 and Q3), the interquartile range (IQR), and then applying the formula for the upper fence. Here’s a quick reminder of the steps:

1. **Sort the data**.
2. **Find Q1** (the first quartile, the 25th percentile).
3. **Find Q3** (the third quartile, the 75th percentile).
4. **Calculate IQR**: \( IQR = Q3 - Q1 \).
5. **Upper fence**: \( \text{Upper Fence} = Q3 + 1.5 \times IQR \).

Let me know if you need help with any specific step, and feel free to upload another problem!

Here are some questions to explore further:
1. What is the formula for calculating the median from a dataset?
2. How do you detect outliers using both the lower and upper fences?
3. Why is the IQR considered a robust measure of spread?
4. How does the upper fence help in fraud detection in your case?
5. Could extreme data points beyond the upper fence indicate abnormal behavior?

**Tip**: The IQR method is especially useful in non-normally distributed data to identify outliers!

The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?

This problem explores fraud detection based on monthly phone usage data, calculating the upper fence using quartiles and IQR. Learn how to identify outliers using statistical methods to determine when a customer should be contacted based on phone use in minutes over 20 months.

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