In this case, this is because the median discards the value 1000 in \(x\), while the arithmetic mean considers it. As we have seen in our example, the mean of \(x\) (133) was much larger than its median (40). This feature of the median can make a big difference. This is because the median basically discards all vector elements except for the most central value(s). While the arithmetic mean considers all the values in a vector, the median value only considers a subset of values. Having defined both types of averages, we can now look into the difference between the two. Let’s see how we can obtain the median in R. We can formalize this in the following way. However, if the list has an even number of elements, we need to determine the arithmetic mean of the two most central numbers. If the list has an odd number of elements, then the median is the most central member in the list. Moreover, we have to differentiate two cases.
This is because in order to find the median, it is necessary to sort the numbers in the list.
While simple to explain, the median is harder to compute than the mean. The median refers to the most central value in a list of numbers.
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