STA2023 Chapter 3 Video 8 IQR And Outliers For Skewed Data
In this 8th video for chapter 3 we're going to take a QR a little farther and see how it relates to outliers for skewed data sets. We've already discussed outliers, a little with our symmetric distributions recall that outliers are unusual values that are far from the main group of data for symmetric data sets. We said that if a value is at two or more standard deviations above or below the mean, then it is classified as unusual or an outlier in histogram typically they're separated from the. Other bins or bars by a space, and we need to look at them closely to know how to treat them if there are mistakes who accidentally mistyped our data entering a computer, they might be removed or corrected. And if they are not mistakes, you might do your statistical analysis two times once with.
And once without the outliers that's something important to note as you proceed through your Moscow lab assignments for chapter 3. And as I as we've already stated when you're using the mean in standard. Deviation with a symmetric distribution.
Outliers are the advantage that our two standard deviations from the mean either above or below. But we need a different way to classify outliers with skewed data, because we don't have a mean and a standard deviation when we're using the median and IQR, where that skewed data outliers are data values, more than 1.5, occur, ours, either below q1 or above q3. We will use these two formulas, q1 minus 1.5 times, the IQR for any lower liars and q3, plus 1.5 times the IQR. For any higher outline let's, look at an example where there may be lower and higher outliers. We've seen these children's heights example before in a previous video, we have a group of 14 children with the following heights. We can see to the game whether there's a big jump 41 to 48. Then 49 51, 53 there's all clustered together.
So 41 might be an outlier because there's a 7-inch gap here. Same thing on the upper side, we're, pretty clustered 58, 60 62 65 and there's this big jump to 76. So 76 might also be. An upper or a higher outlier, we are going to see if there are any outliers. The first thing to define is the IQR, we've already done that call. There are 14 children. We split it.
So there are 7 data pieces on the Left 7, data pieces on the right. 51 was q1. 60 was q3. So the IQR was 9.
And so now to find my possible, lower outliers to see, well is 41 an outliers I'm going to take Q 1, which was 51 and subtract 1.5 times, 9 I. Do that on my calculator type that in all at once gives me 37.5. This is an interest this. Tells me if there are any Heights 37.5 or lower, it is an outlier well, 41 isn't that low.
So 41 it is not an outlier now I need to test my upper in and see. Well is 76 an outlier my upper side. It is q3, which is 60 plus 1.5 times that IQR of none.
If we type that into the calculator, we get seventy-three point five inches. This tells me that any height that is seventy-three point five or above as an outlier since 76 is above that. We can say that seventy-six is an outlier these two values that we just. Calculated the thirty-seven point five and the seventy-three point five, these are known as fences anything within these values is considered typical it's, it's, normal, it's, not unusual. But anything outside the fence like this, seventy-six that would be an outlier.