WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over the box and whisker plot.
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A box and whisker plot looks like this.
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It displays the distribution of data items along a number line.
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We are going to use the box and the whiskers to represent certain items in the data.
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Before I explain this, I want to give you the data set.
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The numbers that I am basing this plot on are 2, 3, 4, 5, 6, 7, and 9.
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Let's say that that is my data set.
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From here, I want to find the median.
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Remember median; the key word for median is middle.
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If the numbers are in order from least to greatest, then I want to find the middle number.
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2, 3, 4, 5, 6, 7, and 9.
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Let me just rewrite it here so I can give myself some room to work with... 6, 7, and 9.
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To find the median, because it is in order from least to greatest, I can just find the middle number.
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3 on this side; 3 on this side; that is my median.
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This is called the median.
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Not including the median, on the lower group of numbers,
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the smaller group of numbers, I want to look for the median again.
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Just from this group right here, just from those three numbers,
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the median, the middle number, is going to be 3.
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That number is called the lower... because it is part of the lower set... lower quartile.
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Same thing for the other side.
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Again between those three numbers, the median is going to be 7.
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That is called your upper quartile.
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All three numbers represent the median.
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This 5 right here, that is the median within the whole set of numbers.
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The lower quartile is the median among the lower half.
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The upper quartile among the upper half.
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The smallest number in your data which is the 2, that number there is called your lower extreme.
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That means this number, the biggest number in your data, is going to be your upper extreme.
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Again we have our median.
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That is the first thing you want to look for, median.
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From your lower half, you are going to find the median again.
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That is your lower quartile; in the upper half, upper quartile.
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Smallest number is your lower extreme.
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Your largest number, the biggest number, is your upper extreme.
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Once you find those numbers, we have five numbers circled there.
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Those are the numbers that are going to be represented in this box and whisker plot.
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The box right here, these three lines in the box,
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this one, this one, and this one, represent your three medians.
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The number right here, this right here is your median of the data.
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This is your median; this right here which is 5; this your median.
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These two right here, this one and this one, the 3 and the 7, are your quartiles.
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This is the lower quartile; this one right here is your upper quartile.
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Those three, your quartiles right here, that is what forms the box.
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All you have to do is once you have the lower quartile,
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you have the upper quartile, then you just draw lines connecting them like that.
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That is how you create your box from the box and whisker plot.
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These right here are called your whiskers.
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Here is you whisker here; the whisker here.
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This number right here is your lower extreme.
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That is the 2; see how it is under the 2.
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This one is your upper extreme.
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That is how we form the box and whisker plot.
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Median, your lower quartiles, that forms the box.
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The whiskers are going to go to your extremes, the lower extreme and then the upper extreme.
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Once you have a set of data, just look for those numbers.
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Once you have them, you can just go ahead and just draw your box and your whiskers.
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The first example, name the median, lower quartile, upper quartile, lower and upper extremes.
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Remember within our box, we look for these numbers here.
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This right here, this is your median.
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The median I am going to say is 8.
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This number here is my lower quartile; lower quartile is 6.
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My upper quartile is 12.
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Then your extremes, that number right there, the whiskers, is going to the 4.
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My lower extreme is 4; my upper extreme is 13.
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We got median, lower quartile, upper quartile, lower extreme, and upper extreme.
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The next one, the information is given to us.
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We just have to draw the box and whisker plot.
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Remember the lower extreme and the upper extreme, that is my smallest number and my biggest number.
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Those are the numbers that are going to be the numbers that my whiskers are going to be drawn to.
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I know my lower extreme is going to go like that.
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I am going to draw a point right there.
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My upper extreme is going to be 12.
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The easiest way to draw the box and whisker plot is to draw the box first.
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My lower quartile is 5.
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I am going to draw a little line like this on 5.
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My upper quartile is 10; that is the median of the upper half.
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Upper quartile is 10; draw line like that.
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My median is 8; 8 right there.
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Remember you want to draw your box; that is going to be the box.
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You don't have to use it in different colors; it could just be like that.
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Just make sure you have these three under the correct numbers.
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Now you can just draw your whiskers.
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From here, you can draw the whisker going out to the 4.
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Here the whisker to the upper extreme; that is 12.
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That is it; that is your box and whisker plot.
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The next example, we are going to find the median,
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the lower and the upper quartiles, the lower and the upper extremes.
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Then we are going to graph it using the box and whisker plot.
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The first thing to do since we have to find the median and the quartiles and the extremes,
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I need to list my numbers out in order from least to greatest, the smallest number to the biggest number.
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Smallest here is 5, then 6, then 7, 8, 8, 9, and 10.
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Let's see, one, two, three, four, five, six, seven.
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One, two, three, four, five, six, seven; just to make sure I didn't miss a number.
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Then I need to find my median; let's see.
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My median will be this right here; this is a median.
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Then I want to find my quartiles.
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Among these numbers, that will be the lower quartile.
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This from here, there is my upper quartile.
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Then my lower extreme; my upper extreme.
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Now I need to graph the box and whiskers plot.
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I need a number line first.
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My largest number is 10 so I have to make sure I cover up to 10 on the number line.
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
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My median is 8; draw a little line like that under 8.
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My lower quartile is 6; my upper quartile is 9.
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Once you have your three little lines right there, draw the box that connects those quartiles.
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My lower extreme, from the box, I am going to draw a whisker out to that lower extreme, 5.
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From here, whisker out to the upper extreme which is 10.
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That is it for this one.
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The fourth example, we are going to draw a box and whiskers plot for this set of data.
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Again we are going to find the median.
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The way we do that is to list numbers out from least to greatest.
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The key word for median is middle.
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Smallest number, 2; we got 2; then the 3; we have 4; another 4.
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Then we have 6; then two 7s; 7, 7, 8, 9, 10, and 11.
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I have one, two, three, four, five, six, seven, eight, nine, ten, eleven numbers.
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One, two, three, four, five, six, seven, eight, nine, ten, eleven.
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Now I need to look for my middle number, the median.
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Let's see, one, two, three, four, five; we count five this way.
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One, two, three, four, five; that leaves me with this number in the middle.
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Remember if you have two numbers in the middle,
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you have to find the average of those two numbers.
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Let's say I had an extra number on this side.
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6 and 7, if those were my middle numbers,
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I would have to find the middle number between 6 and 7.
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Again this is when you have an even number of numbers in your data.
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Then your median, you have to find the middle number between the two numbers in the middle.
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You can do that by adding those two numbers together and dividing it by 2.
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You are finding the average, the mean, within those two numbers.
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In this case, we have only one number so that is our median.
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Then from the lower set of numbers, I look for my median again.
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The middle number is 4; remember that becomes our lower quartile.
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From the upper set, I have the 9; that is going to be my upper quartile.
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My smallest number which is 2 is my lower is my extreme.
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My largest number is my upper extreme.
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Once I have those five numbers, I can draw my box and whiskers plot.
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I am going to draw a number line.
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My largest number is 11.
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I have to make sure I cover up to 11 on this number line.
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, one more, 12.
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1, 2, 3, 4, 5, 6, 7...
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I want to first draw my median.
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On 7, I am going to draw that little line right there under 7.
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Then your quartiles; the 4 like that; another one under 9.
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Remember the quartiles are going to form your box.
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Let's just draw a box like that.
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Once you have your box, we need to draw our whiskers.
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From this end, I am going to draw a whisker out to the lower extreme which is 2.
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Draw a whisker out there.
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On this side, my upper extreme is 11.
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Draw the whisker out to 11 right there; that is it.
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Remember these three are going to represent your medians.
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This is the median of your data.
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These two are the medians of the lower and upper halves.
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That is going to form your box.
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Your whiskers, draw it out to the lower extreme, the smallest number.
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This whisker, upper extreme which is the largest number.
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That is it for this lesson; thank you for watching Educator.com.