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Problem 31 Easy Difficulty

When is the median the most appropriate measure of central tendency?


The median is most appropriate when there are extremes in numerical data , because the mean is influenced by extremes, and the median is not. It is easily calculated when the number of data is not great
(i.e. when sorting is not a difficult task). Also, it can be found in situations when the data are not numerical.
(see text following example 8 )


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Video Transcript

this question asks Win, Is it appropriate to use the median as a measure of central tendency? Well, we knew that we've got to measures of central tendency right now, mean and media, when you have a distribution, a range of numbers that has looks like this, a lot of numbers closer to the middle and fewer numbers in the outside's the median, which I'll call em, and the Mean X bar are going to be about the same when it's symmetrical like this. We call this a symmetrical distribution, but consider what happens when we have a distribution that looks more like this where we have most of our values here, but a couple extreme values way out here. What happens then? Well, the median we know is just the middle, right? So it doesn't really matter where the high values are and where the low values are. The median will always stay the same, so the media will still be in the middle of that big bump. But the mean does depend on extreme values. In fact, extreme values, uh, haven't even greater effect on the mean. Then average values do so when you have values that are way out here in the tails of the distribution is going to affect the mean and bring it closer to the tails. That means when we have distributions like this with extreme values, the median is a better measure of central tendency.