In our case, the order of the numbers is 1, 2, 3, 4, and 5. Find the median of the data set. The median is the middle number in an ordered data set. This is why we lined up all the numbers in Step 2.
For the data set in our example, 3 is the number that's exactly in the middle, and therefore is our median. The median is also called the second quartile. In a data set with an odd amount of numbers, the median will always have the same amount of numbers on either side of it. For the data set 1, 2, 3, 4, 5, the median number, 3, has 2 numbers before it and 2 numbers after it.
That's how we can be sure that it's our median. What if the data 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, 10, 14, 15?
You find the median here by taking the two middle numbers and finding their average. In our example, you would take 7 and 9 — the two middle numbers — add them up and divide them by 2. The median of this data set would be 8. Find the first and third quartiles. We've already found the second quartile of the data set, which is our median.
Now we need to find the median of the lower half of the data set; in our example it would be the median of the two numbers to the left of 3. Do the same to find the median of the two numbers to the right of 3. 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.
Mark your first, second, 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.
Make a box by drawing horizontal lines connecting the quartiles. Connect the top or the first quartile to the top of the third quartile, going through the second quartile. Connect the bottom of the first quartile to the bottom of the third quartile, making sure to go through the second quartile.
Find the smallest, and then the largest, numbers in your data set and mark them on the plot line. Mark these points with a small dot. In the case of our example, the lower outlier is 1 and the upper outlier is 5. Connect your outliers to the box with a horizontal line. The straight line that connects the outliers is informally called the "whiskers" of the box and whiskers plot.
Look at a box and whiskers plot to visualize the distribution of numbers in any data set. You can easily see, for example, whether the numbers in the data set bunch more in the upper quartile by looking at the size of the upper box, as well as the size of the upper whisker.
Box and whisker plots are great alternatives to bar graphs and histograms. The upper quadrant would be the set of numbers to the right of your median, if they are in order from least to greatest. Not Helpful 45 Helpful What is the median for the set of numbers 0, 2, ,2 3, 4, 6, 6, and 12? The data is ordered, so you just need to find the median or center. When there is an even number of observations data points , the center is not necessarily part of the data set.
That is the case here. Three and 4 are in the middle of the data set but the center point comes halfway between 3 and 4, so it would be 3. Not Helpful 41 Helpful What happens if the median of the first quartile is higher than your range of numbers?
Then your first quartile is higher than your range. It doesn't make anything "happen". It doesn't matter either way, as range is not used when making a Box-and-Whisker Plot. Not Helpful 35 Helpful What if I have an even amount of numbers, and the two middle numbers are the same?
The median is the middle number or the average of the two numbers if you have an even amount of numbers. If you have two that are the same, you do not need to average since they are the same. If they weren't, you would average the two to get the median. Not Helpful 21 Helpful If the same value is shown multiple times, do we write it that number of times or just once?
You would write the number as many times as it occurs to make the results accurate. The lower extreme should be the lowest number in the data set, or the minimum number. Not Helpful 16 Helpful When I have an even number of data set, do I need to include the median numbers?
Yes, you just have to find the average of the two medians or middle numbers. Find the average of these two numbers to get the ultimate median of 4. Not Helpful 25 Helpful The whisker is just the line that connects the two points on the side of your box, which are your highest and lowest number in your data set. Not Helpful 14 Helpful I'm still confused about how to do these.
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Box-and-whisker-plot or diagram is a way of representing minimum value of data, first quartile, median, second quartile and maximum value of data.
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