How to Plot Outliers on Whisker Plots
In this video lesson, let’s learn how to identify and plot outliers. So the table shows us the ages of the last 21 presidents when they first took office. So we’ve got three rows of seven ages each. We need to make a box and whisker plot of this data but we have to consider the outliers as well.
So here’s what we’re going to do. First thing I’ve done, is I’ve arranged the data in increasing in order. So I’ve arranged the data in increasing order to make life a little easier for us. Start over the lowest value which is 42 and the highest value is the last one which is 69. And we’ve arranged all the values in increasing order. So the first thing when we create a box in whisker plot, we need three things. We need the median, we need the lower or the first quartile and we need the upper or the third quartile. What is the median? Median is the center value. How many numbers do we have? 21, right? So the 11th value will be the median, 11th value which is one, two, three, four, five, six, seven, eight, nine, ten, eleven. So this is the median which is center. Why 11th? I’ve got then numbers on the left and ten on the right, so the median in 54.
So if this is the median, the first quartile or the lower quartile is the center of this, center of this is five numbers to the left, five numbers to the right which is this. Center on this side is 56. Okay? All I’m doing I dividing it at the median and again looking at the middle number on both sides. So the lower quartile is 51, upper quartile is 56.
The lower quartile is the average of 51 and this upper quartile is the average of 50 and 60 which would be 58. Let me just erase this. The upper quartile will be the average of 56 and 60 because I’ve got one, two, three, four, five, six, seven, eight, nine, ten numbers right? So then upper quartile is 58, so that’s what we know. Median 54, lower quartile 51, upper quartile is 58.
The difference between these two quartiles which is the difference of interquartiles is 58 minus 51 which is the interquartile difference is seven. Remember, before we draw on box on whisker plot, we also need to look at something called an outlier. An outlier is something that is 1.5 times the difference. Let me explain to you what that means. The lowest value here is 42, the highest value is 69. What we look at is what’s the difference between 1.5 times the difference, is 1.5 times 7 which is 10.5. So what we want to look at is there any value which is between 10.5 of this and this. So 51 which is the first quartile minus 10.5, is 40.5, that is the lower extreme and then 58 plus 10.5 is 68.5 which is the higher extreme.
So what we would want to do when we draw a box on whisker plot is only considered these as the extremes. So here is what we do, we will draw a number line starting with 42 ending with 69. What values will be put? 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, I’m just going to number these real quick. You got the idea right? So let’s do this as well. That’s our number line. So what is the first quartile? 51, right? That’s the first quartile, third quartile is 58. So the box is between these two and the whiskers will go from 42 but this one will only go to 68.5 because that’s the highest value. 69 will be an outlier because it lies — it’s a number way out there.
The way we computed that again is we looked at the first and third quartile, looked that the difference, the difference was seven, all right? Multiplied 7 by 1.5 to get ten and a half. We looked at a number that’s ten and a half over, ten and a half over here. Anything that was more than one and a half times the size of the box is called an outlier. That’s what we were supposed to do, draw a box in whisker plot which we did but we wanted to make sure we plot the outlier as well.
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