Box and Whiskers Plot

For our first video lesson, I thought we should do something visual. Let's try our hand at some graphing.

This lesson covers how to draw a box and whiskers plot given a set of data.

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transcript:

In this video I'm going to show you how to draw a box and whiskers plot. A box and whiskers plot helps to show you how a certain set of data is distributed among its points. I want to start with an example - 22, 23, 25, 27, 28 and 32. Check to see that the numbers are in order from least to greatest. And if they're not, you're going to have to rearrange them. For example we're lucky they are in order from least to greatest so we're ready for our next step.

We're looking for three specific points here. We're looking for our median, our lower quartile and upper quartile. The median just means the middle number. We'll find that first. To find the median, the middle number, let's count up all the numbers we have. One, two, three, four, five, six, we're going to divide that by two. Six divided by two is three. So we know the median is between the third and the fourth number. Right here.

When you have an even set of data, you have two middle numbers, 25 and 27 are both our middle number because there's two on either side of those. We need to find the average of those two middle numbers. The average of 25 and 27 is 26. If we had an odd set of numbers which we'll see in a second, we'd still divide however many numbers we have by two. And then round that number up.

For example, if we had one more number, say 34 in our set. We now have one, two, three, four, five, six, seven numbers. Seven divided by two is 3.5 - rounds up to four. So the fourth number would be the median in that case. One, two, three, four, 27.

And you can see three on the left of 27, three on the right of 27. It lets you know that 27 is your middle number. So let's just go ahead and get rid of 34 for now. We're going to find the lower quartile by finding the middle number of the first half of the numbers we have. That's why I do that line. It's a little helpful to separate the two halves of data. The middle number here is obviously 23. But you could still do the same processes before if you have a larger set of numbers.

Three numbers divided by two is 1.5, rounds up to two. So the second number is our lower quartile, 23. The upper quartile is found the same way as the lower quartile. Except you're going to look at the second half of data. In this case, 28 is the middle number.

All right. Now we have the basic information we need to draw our box and whiskers plot. And next we're actually going to draw the plot. To draw the box and whiskers plot, we want to draw a number line to represent data. The number line needs to be long enough to include the smallest number and biggest number.

We also want to make sure we draw the scale or else our box and whiskers plot isn't going to be an accurate representation of the data we have. I'm just going to go by 1's on this number line because we have such a small set of data.

But you could feel free to go by any scale you'd like which will help you represent the numbers as best as you can. As a refresher, our numbers were 22, 23, 24, 25, and so on all the way up to 32. We want to look back at our median, the lower quartile and the upper quartile and put a dot above the the number line at each of those places.

Our median was 26. So we have to put a dot up here at 26. Our lower quartile was 23, so another dot goes there. And the upper quartile was at 28. Twenty seven, 28. So a dot goes there. We have two more dots and those are just smallest number and the biggest number for the data. So 22 and 32.

Next we want to draw a vertical line that goes through our median, the lower quartile and the upper quartile. And this is going to be the basis of our box. So you're just going to connect those three lines in order to form a box. For the whiskers part, we're just going to draw a line out from the box to our biggest number and our smallest number. And that is your box and whiskers plot.

I hope this video was helpful. But if you need more help with this or other topics, visit www.yourtutoronline.com to find a tutor. Yourtutoronline.com provides online tutoring services in the virtual classroom you just saw on this video. Thanks for watching!