[DATA] Fraud Detection As part of its “Customers First” progra...

Question

[DATA] Fraud Detection As part of its “Customers First” program, a cellular phone company monitors monthly phone usage. The program identifies unusual use and alerts the customer that their phone may have been used by another person. The data below represent the monthly phone use in minutes of a customer enrolled in this 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?

Accepted Answer

Welcome back, everyone. A company tracks the number of daily page views in thousands for a product over 12 days and flags, unusual spikes using the upper fence. The data is given below. What is the upper fence or cut off above which a day should be flagged. So for this problem, let's understand that we're looking for outliers, right, and specifically the upper funds. So what we want to do is simply remember that an outlier would be a data value X. Which is greater than. The third quartile plus 1.5 multiplied by the interquartile range, right? This is for the upper fence. So in this problem we simply want to identify the 3rd quartile and the interquartile range. We want to sort our data in ascending order. We have a total of 12 data points, and now if we sort them, we start with 60. Followed by 62, 65, 68. 7 7273. 7576. 80 And then we have 2 more, right? So those would be 82. And 140. So this is our sorted data set. And now because we have a total of 12 data points, we begin by splitting this data set in half, right? So, 123456. So we have 6 data points on the left, 6 on the right. From here, we can identify interquartile range. Let's remember the formula for IQR. Specifically, it is equal to the 3rd quartile minus the 1st. Quartile. How do we identify these? Well, let's focus on the first half of our data set. We have 123456 data points, and we want to identify the median. So now since we have an even number of data points, the median value is going to be The mean of the two middle values. So Q1 is going to be the average of 65 + 68. We're going to add them and divide by 2. This is equal to 66.5. And similarly, we can identify the third quartile by considering the right half of the sorted data set. We take the average of 76 and 80. Which gives us 78. So now the interquartile range IQR is going to be Q3 minus Q1, according to the formula. We take 78 and we subtract 66.5. We get 11.5. So now we're going to identify that boundary that gives us the outliers for the upper fence. We can essentially say that the cutoff would be X greater than Q3, which is 78. Plus 1.5 multiplied by. 11.5. This is equal to 95.25, but essentially, since we're looking at the whole numbers, we can say that Any number greater than 95 would be our cutoff, so the answer would be 95. Let's label it and thank you for watching.

Key Concepts

Interquartile Range (IQR)

Quartiles (Q1 and Q3)

Upper Fence for Outlier Detection

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