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Worked example: Creating a box plot (even number of data points)

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UNC‑1.L.1 (EK)
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CCSS.Math: ,
Learn how to create a box plot. The data set used in this example has 14 data points.

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  • duskpin seed style avatar for user 563484
    can i get some help what does IQR mean
    (7 votes)
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  • hopper jumping style avatar for user Markarino /TEE/DGPE-PI1   #Evaluate
    I'm confused. In the last worked example when we had an odd number of data, we were taught to eliminate the mean when calculating the upper and lower means. Does that rule not apply with even numbers of data? That was not clear.
    (2 votes)
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    • cacteye blue style avatar for user Jerry Nilsson
      We want the median to divide the data set into two equal halves.
      However, with an odd number of data points the two halves can't be equal in size which is why we remove the median before we calculate the upper and lower quartiles.
      With an even number of data points we don't have this problem and don't have to remove the median.
      (3 votes)
  • aqualine ultimate style avatar for user 𝕵𝖆𝖓𝖊
    How do I get a profile photo?
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    • leaf grey style avatar for user Deleted_User
      Hang on. This is an off-topic question, so if it doesn't have anything to do with the subject (box + whisker plots), then you can just search for it in the search box at the top of the page. You get a profile photo by tapping the picture on the left of your bio on the "edit profile" section.
      (2 votes)
  • aqualine sapling style avatar for user JEFFERYS
    sleep ideas or can you give me some
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  • blobby green style avatar for user Arbaaz Ibrahim
    When working out the median of the first and second half, why did Sal include the 4 and 5?
    (2 votes)
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    • cacteye blue style avatar for user Jerry Nilsson
      The amount of data points that are less than the median is always equal to the amount of data points that are greater than the median.

      In this case we have an even number of data points, namely 14 of them, and so the median should be somewhere between the 7th and 8th data points (i.e. between 4 and 5).
      We arrange this by letting the median be the mean of those two data points ((4 + 5)∕2 = 4.5).

      – – –

      When working out the lower quartile we use the same logic, but for the data points up to and not including the median (i.e. all the data points less than 4.5, which does include 4).

      Similarly, for the upper quartile we consider the data points above the median (greater than 4.5, thus including 5).
      (2 votes)
  • leafers seed style avatar for user Stacie Shiroma
    I dont know how to create a box plot from a histogram. Help please!
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  • ohnoes default style avatar for user sunshinehappyrainbow127
    I'm not really sure about the next worksheet. Can someone help me?
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  • starky seedling style avatar for user andrew.mettlen927
    what does iqr mean:)
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  • ohnoes default style avatar for user Tankman
    what does iqr mean
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  • mr pants orange style avatar for user Isr
    The header in the video states to exclude the median when computing the quartiles. But Sal doesn't exclude them in the video.
    (0 votes)
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    • cacteye green style avatar for user Nights Dawn
      The median was excluded. It was 4.5 (the mean of 4 and 5).

      If the calculated median is the same as one of the data points, it would be excluded.

      In this case it was between two data points, so data points 4 and 5 were not excluded when determining the quartiles.
      (2 votes)

Video transcript

- [Voiceover] Represent the following data using a box-and-whiskers plot. Once again, exclude the median when computing the quartiles. And they gave us a bunch of data points, and it says, if it helps, you might drag the numbers around, which I will do, because that will be useful. And they say the order isn't checked, and that's because I'm doing this on Khan Academy exercises. Up here in the top right, where you can't see, there's actually a check answer. So I encourage you to use the exercises yourself, but let's just use this as an example. So the first thing, if I'm going to do a box-and-whiskers, I'm going to order these numbers. So let me order these numbers from least to greatest. So let's see. There's a one here, and we've got some twos. We've got some twos here and some threes, some threes, some four-- I have one four and fives. I have a six. I have a seven. I have a couple of eights, and I have a 10. So there you go. I have ordered these numbers from least to greatest, and now, well just like that, I can plot the whiskers, because I see the range. My lowest number is one. So my lowest number is one. My largest number is 10. So the whiskers help me visualize the range. Now let me think about the median of my data set is. So my median here is going to be, let's see. I have one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14 numbers. Since I have an even number of numbers, the middle two numbers are going to help define my median, because there's no one middle number. I might say this number right over here, this four, but notice, there's one, two, three, four, five, six, seven above it, and there's only one, two, three, four, five, six below it. Same thing would have been true for this five. So this four and five, the middle is actually in between these two. So when you have an even number of numbers like this, you take the middle two numbers, this four and this five, and you take the mean of the two. So the mean of four and five is going to be four-and-a-half. So that's going to be the median of our entire data set, four-and-a-half, four-and-a-half. And now, I want to figure out the median of the bottom half of numbers and the top half of numbers. And here they say exclude the median. Of course I'm going to exclude the median. It's not even included in our data points right here, because our median is 4.5. So now let's take this bottom half of numbers. Let's take this bottom half of numbers right over here and find the middle. So this is the bottom seven numbers. And so the median of those is going to be the one which has three on either side, so it's going to be this two right over here. So that right over there is kind of the left boundary of our box, and then for the right boundary, we need to figure out the middle of our top half of numbers. Remember, four and five were our middle two numbers. Our median is right in between at four-and-a-half. So our top half of numbers starts at this five and goes to this 10. Seven numbers. The middle one's going to have three on both sides. The seven has three to the left, remember of the top half, and three to the right. And so the seven is, I guess you could say the right side of our box. And we're done. We've constructed our box-and-whiskers plot, which helps us visualize the entire range but also you could say the middle, roughly the middle half of our numbers.