Investigating outliers

0:00- [Instructor] We're told for each situation, describe how to determine whether to keep or remove the outlier when analyzing the data. So why don't you read through this, and pause the video, and see if you can think this through a little bit. Okay. Now let's look at scenario A.

0:15The dot plot represents the distribution of the number of live concerts attended in the past year by a group of 20 students. All right, so each of these dots is how many concerts the student attended. So for example, three students went to no concerts. It looks like, what is this?

0:32Five students went to one concert. And what looks like an outlier, or it is an outlier, that we immediately spot is this one over here. At least the data that I'm looking at right over here is that one student said they attended 16 concerts. So the first thing to think about when you see outlier data like this is to say, "Is it even possible that someone went to 16 concerts?"

0:54Well, that's a lot of concerts, but it is possible to go to 16 concerts. If this said something like 400 concerts, I was like, "Oh, they'd have to go to more than one concert a day and they're going to school. I should really double click on that." But this one, it is possible.

1:09If you know the student who answered this question, you could even go to them and say, "You really went to 16 concerts?" And they say, "Yes." And if they say, "These are the concerts I went to." They might've said, "Oh, I thought you asked how many hot dogs I ate last year."

1:21Then you would say, if they said something like that, then you would remove it because this would be an error here and you would actually try to record what the data is. But just based on the information that we've been given, even though this is an outlier, you would keep it in the data.

1:35There is a student who went to 16 concerts. So you don't just remove outliers just because it's very different than everything else. If it's real data, it's real data. You should include it. Now in Scenario B, a board game spinner has sections labeled one through eight.

1:52After spinning it 15 times, Mei recorded her data. Well, what's interesting here is the outlier is this 18. Somehow, we have recorded in the data or that Mei has recorded in her data, that an 18 was recorded in these spins, which is impossible. This is impossible.

2:14So if you see data that is clearly impossible, you might say, "Well, why did it happen?" Well, it might have been an error. Maybe she spun it 16 times and it was a one and an eight. But if we don't really know what's going on and it's something is truly impossible like this, the most prudent thing would be to remove that data and then just have the 14 data points here, or maybe even reconduct the experiment or collect some new data.

2:41So outliers are places to look at. Some of these others might have been mistakes too, we don't know. But the outlier, like this, is a clear example of something that could not have happened and you should remove it.