Draw a Box-and-whisker Plot of the Data

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A box and whisker plot is a diagram that shows the statistical distribution of a set of data. This makes it piece of cake to come across how information is distributed along a number line, and it'southward easy to make ane yourself!

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1. i

   Gather your information. Let'southward say we start the numbers 1, iii, 2, four, and 5. These volition be used for calculation examples.

2. ii

   Organize the information from to the lowest degree to greatest. Have all your numbers and line them upwardly in order, so that the smallest numbers are on the left and the largest numbers are on your correct. In our case, the order of the numbers is 1, ii, 3, 4, and 5.^[1]

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3. iii

   Find the median of the information set. The median is the eye number in the data fix when the data fix is written from to the lowest degree to greatest. (This is why we lined upwardly all the numbers in Step 2.) For the data fix in our example, 3 is the number that'southward exactly in the middle, and therefore is our median. The median is also chosen the second quartile.^[2]

   • In a data set up with an odd amount of numbers, the median volition e'er have the same amount of numbers on either side of information technology. For the information set 1, 2, 3, 4, v, the median number, 3, has two numbers earlier it and 2 numbers after it. That's how we can exist certain that it's our median.
   • What if the information set you're working with has an even amount of numbers? What if you had to find the median of 2, 4, 4, 7, 9, x, 14, 15? You find the median here by taking the two middle numbers and finding their average. In our example, you would take seven and 9 — the ii center numbers — add them upward and divide them by 2. 7 + 9 equals sixteen, and 16 divided by 2 equals 8. The median of this information set would be 8.

4. iv

   Detect the first and tertiary quartiles. We've already found the 2d quartile of the information set, which is our median. At present nosotros need to find the median of the lower one-half of the information fix; in our instance information technology would be the median of the two numbers to the left of 3. The median of 1 and ii is (1 + 2) / 2 = 1.5. Practise the aforementioned to find the median of the two numbers to the correct of 3. (iv + 5) / two = 4.5.^[3]

5. v

   Draw a plot line. This should be long enough to contain all of your data, plus a little extra on either side. Make sure to place the numbers at even intervals. If you're dealing with decimals, such as 4.v and ane.five, be certain to label them as well.

6. 6

   Mark your kickoff, 2nd, and third quartiles on the plot line. Take the values of your first, second, and third quartiles and make a mark at those numbers on the plot line. The mark should be a vertical line at each quartile, starting slightly above the plot line.^[4]

7. 7

   Brand a box past drawing horizontal lines connecting the quartiles. Connect the top or the kickoff quartile to the height of the tertiary quartile, going through the second quartile. Connect the bottom of the offset quartile to the bottom of the tertiary quartile, making sure to go through the second quartile.^[five]

8. viii

   Mark your outliers. Find the smallest, and then the largest, numbers in your data set and mark them on the plot line. Marker these points with a pocket-size dot. In the example of our example, the lower outlier is one and the upper outlier is five.^{[half dozen]}

9. 9

   Connect your outliers to the box with a horizontal line. The straight line that connects the outliers is informally chosen the "whiskers" of the box and whiskers plot.

10. ten

    Finished. Look at a box and whiskers plot to visualize the distribution of numbers in whatsoever data prepare. You can easily see, for example, whether the numbers in the information set bunch more than in the upper quartile by looking at the size of the upper box, besides as the size of the upper whisker. Box and whisker plots are great alternatives to bar graphs and histograms.^[7]

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Add New Question

• Question

  How practise you know what the upper quadrant is?

  

  The upper quadrant would exist the ready of numbers to the right of your median, if they are in order from least to greatest.

• Question

  What if I have an fifty-fifty amount of numbers, and the two middle numbers are the same?

  

  The median is the middle number or the average of the ii numbers if yous take an even amount of numbers. If y'all have two that are the aforementioned, you do non demand to average since they are the same. If they weren't, you would average the two to become the median.

• Question

  What'south the lower extreme?

  

  The lower farthermost should be the lowest number in the information ready, or the minimum number.

• Question

  What is the median for the set of numbers 0, 2, ,ii 3, 4, 6, half dozen, and 12?

  

  The data is ordered, so y'all just need to find the median or middle. When in that location is an even number of observations (data points), the center is non necessarily role of the data set. That is the case hither. Three and four are in the centre of the data set but the center point comes halfway between 3 and 4, and then it would be 3.5.

• Question

  What happens if the median of the beginning quartile is college than your range of numbers?

  

  Then your first quartile is higher than your range. Information technology doesn't brand anything "happen". It doesn't affair either manner, every bit range is non used when making a Box-and-Whisker Plot.

• Question

  If the same value is shown multiple times, do nosotros write it that number of times or just once?

  

  You would write the number every bit many times equally it occurs to make the results accurate.

• Question

  How to calculate the whisker in the box plot?

  

  The whisker is merely the line that connects the two points on the side of your box, which are your highest and lowest number in your data gear up.

• Question

  When I have an even number of data set up, do I demand to include the median numbers?

  

  Yeah, y'all just take to find the average of the two medians or centre numbers. For case, if the number set is {ane,two,3,4,5,five,6,8}, and so the two middle numbers would be 4 and 5. Detect the average of these two numbers to get the ultimate median of 4.5.

• Question

  I'thou all the same dislocated near how to do these. Are they similar to histograms?

  

  No, they are not. A histogram u.s.a. used to show frequency tabular array data. These plots are used to testify quartiles.

• Question

  How do I find the outlier of the plot?

  

  The outliers are just the greatest and smallest numbers in the set.

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Article Summary Ten

To make a box and whisker plot, start by organizing the numbers in your information set from to the lowest degree to greatest and finding the median. And so, observe the commencement quartile, which is the median of the beginning of the information ready, and the third quartile, which is the median of the terminate of the information set up. Once you've done that, draw a plot line and mark the quartiles and the median on it. Finally, connect the quartiles and median with horizontal lines to make a box, and then mark the outliers. To learn how to interpret a box and whisker plot, roll down!

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