Resistant Measures Listed below are 10 wait times (minutes) fo...

Question

Resistant Measures Listed below are 10 wait times (minutes) for “Rock ‘n’ Roller Coaster” at 10 AM (from Data Set 33 “Disney World Wait Times”). The data are listed in order from lowest to highest. Find the mean and median of these ten values. Then find the mean and median after excluding the value of 180, which appears to be an outlier. Compare the two sets of results. How much was the mean affected by the inclusion of the outlier? How much is the median affected by the inclusion of the outlier?

15 20 25 30 30 35 45 50 50 180

15 20 25 30 30 35 45 50 50 180

Accepted Answer

Welcome back, everyone. In this problem, the wait times in minutes for a popular theme park ride at 3 p.m. are listed in increasing order 1218, 22, 28, 30, 34, 40, 48, 52, and 170 minutes. Find the mean and median of these 10 values. Excluding the value 170, which appears to be an od layer, find the mean and the median of the remaining data. How were these statistics affected by the o layer? Now let's focus on the first part of this problem. Let's find the mean and the median for these 10 values. Remember that to find a mean, we would add all of these values and divide by the number of values. In this case, 10, OK? So now the mean. X bar is going to be equal to the sum of values divided by the amount of values, which in this case, OK, is gonna be 12 + 18 + 22 + 28. Plus 30 + 34 + 40. Plus 48 + 52 + 170, OK, all divided by 10. Now, when we add these values up, it's equal to 454 and 454 divided by 10 is equal to 45.4. So the mean of our data set is 45.4 minutes. Next, let's find the median. Now remember that the median will be the value that's in the middle when our numbers are or when the data is arranged in order, whether ascending or descending. If we look at our data here, it's already arranged in order, OK, from smallest to largest in ascending. So here, since there are 10 values, the median will be the average of the 5th and 6th value. If we start to count. The 1st, 2nd, 3rd, 4th, 5th value is 30, while the 6th value is 34. Therefore, The median Is going to be equal to the average of 30 and 34, so that's 30 plus 34 divided by 2. That's 64 divided by 2, which equals 32. So the median is 32 minutes. Now notice that in the second part of our problem, we're basically going to find the mid and the mean and the median again, but we're excluding the value of 170. So excluding The old layer 170. We're going to repeat the process, but it's just that we won't have 170 in the mix. So now the mean then is going to be equal to the sum of values. In this case, I could basically copy the sum, OK. But when I write it down here, all I'm going to do is to remove the 170, OK? So it's all of this except 170, and no, because I have removed one value, that means the number of values here is going to be 9, not 10, OK? So it's gonna be all of this divided by 9. When I add these values, OK, it's equal to 284. Divided by 9. Let me put this back in blue, which is gonna be equal to 31 or approximately equal to 31.6. OK? So the mean here is 31.6 minutes. On the other hand, the median. OK, is now going to be the 5th value because remember it's now if we take out 170, OK, now we're gonna have 9 values and if we take a quick check, OK, the number, the 5th number will be in the middle. So that's 12345, therefore, our median will be 30, OK? So our median value is 30 minutes. Now what do you notice when we compare the results now that we've removed the old layer? No, the mean has dropped from 45.4 to 31.6, so that shows a significant decrease due to the oat layer. The median also, sorry, that was the mean, my apologies, and the median changed from 32 to 30 minutes showing only a slight effect. So this shows that the median. OK, the median. Is more resistant. The Oliers Than the me Meat is more resistant to oat layers than the meat. Thanks a lot for watching everyone. I hope this video helped.

��app

Key Concepts

Mean

Median

Outliers

Watch next