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?

359359

511511

480480

488488
 
342342

339339

506506

365365

524524

325325

404404

500500

495495

338338

475475

332332

499499

424424

392392

510510

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Part 1

The cutoff point is 

enter your response here 

minutes.

​(Round to the nearest​ minute.)

numbers given: 359, 342, 524, 495, 499, 511, 339, 325, 338, 424, 480, 506, 404, 475, 392, 488, 365, 500, 332, 510

To find the cutoff point using the upper fence, we can use the following steps:

1. **Calculate the Quartiles (Q1 and Q3)**:
   The upper fence is defined as \( \text{Q3} + 1.5 \times IQR \), where the IQR (Interquartile Range) is \( \text{Q3} - \text{Q1} \).

2. **Find the Interquartile Range (IQR)**:
   - Q1 is the 25th percentile.
   - Q3 is the 75th percentile.

3. **Use the Formula for the Upper Fence**:
   \[
   \text{Upper Fence} = Q3 + 1.5 \times IQR
   \]

I'll compute this step-by-step.The calculated values are as follows:
- Q1 (1st quartile): 355 minutes (rounded to nearest minute)
- Q3 (3rd quartile): 499 minutes (rounded)
- IQR (Interquartile Range): 145 minutes (rounded)
  
The cutoff point, using the upper fence formula, is:

\[
\text{Upper Fence} = 499 + 1.5 \times 145 = 716 \, \text{minutes}
\]

So, the cutoff point is **716 minutes**.

Would you like further clarification, or do you have any questions? Here are five related questions:

1. What happens if the customer's usage exceeds the upper fence?
2. How does the lower fence compare to the upper fence?
3. Can the upper fence be adjusted for different quartile calculations?
4. How does the concept of IQR help in detecting outliers?
5. Would trimming the dataset affect the upper fence?

**Tip**: The interquartile range (IQR) is a great way to detect outliers without being overly influenced by extreme values in the dataset.

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?

359, 511, 480, 488, 342, 339, 506, 365, 524, 325, 404, 500, 495, 338, 475, 332, 499, 424, 392, 510

The cutoff point is ___ minutes. (Round to the nearest minute.)

Learn how to calculate the upper fence using the interquartile range (IQR) to detect outliers in phone usage data. This problem provides step-by-step guidance to compute the cutoff point based on a dataset of 20 months of phone usage. Suitable for high school students (Grades 9-12).

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