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What is the Median of a Data Set?

What is the median of a data set?

Summary

  1. The median is the middle number in a data set when the data points are in numerical order
  2. The example on the right has an EVEN number of data points
  3. To find the median, we take the average of the two middle numbers, 6 and 10
  4. In the last example, 275 is an outlier
  5. The mean isn't a good measure here, because it is larger than all the numbers in the data set except for the outlier!
  6. The mode isn't a good measure here either, because it is the smallest number in the data set

Notes

    1. It doesn't matter if the data points are in order from least to greatest or greatest to least
    2. The same number will be in the middle either way
    1. To find the middle number, just count inward from the beginning and end of the list
    2. You can see that there are 3 numbers bigger than 7 and 3 numbers smaller than 7
    3. So 7 lands right in the middle!
    1. Our example from before had 7 data points, which is an odd number
    2. So when our data was in order, all we had to do was pick out the middle number, which was 7!
    1. If you have an even number of data points, you still need to put the numbers in order first
    2. But if you have an even number of points, there will be TWO numbers that fall right in the middle
    3. Since we can't have two medians, we want to figure out what number comes right in between them
    4. To do this, we can take the average of the two middle numbers
    5. This means that the median won't always be one of the original data points, but that's okay!
    1. Measures of central tendency summarize data sets by finding a number that is close to most of the points in the data set
    2. Mean, median, and mode are all examples of measures of central tendency
    3. Depending on your data set, sometimes one of these works better than the others
    4. The best measures of central tendency are close to most of the points in the MIDDLE, or CENTER, of the data set
    1. An outlier is a data point that is much bigger or much smaller than all the other points in the set
    1. If you have an outlier in your data set, the mean will be skewed toward that outlier
    2. So if your outlier is much bigger than the rest of the data points, your mean will be bigger than most of your data points as well
    3. If your outlier is much smaller than the rest of the data points, your mean will be smaller than most of your data points
    4. In our example the mean, 96, is larger than all the points in our data set EXCEPT the outlier!
    5. So it's not a very good representation of our data set!
    1. The mode, the most common number in our data set, is 52
    2. That's a lot smaller than most of our data points!
    1. Since most of our numbers are between 65 and 90, a good measure of central tendency should be somewhere in that range
    2. The median is 81, which falls right in the middle of that!
    3. So here the median is the best measure to use to summarize the data set