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Discuss the advantages and disadvantages of the mean as a measure of central tendency.

The mean has the advantages of:

- being easy to calculate,

- taking all data into consideration,

- being reliable (repeated samples are likely to give similar means)

A hungarian joke here to illustrate the point: "If one man eats meat, and another potatoes, on average they both eat goulash (stew of meat and potatoes)."

Multivariable Optimization

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Campbell University

Oregon State University

Harvey Mudd College

Baylor University

this question. Ask you to consider the pros and cons of using the mean as a description of central tendency. So we know that the mean is essentially adding up all of the data and dividing by how many data points there are, Um, we right, that is, that some of X over n equals X bar. So the mean is just the average of all the data points. What's what sort of the average? Well, there's a couple pros right away we know is pretty easy to calculate. Um, there are a lot of like calculators they confined online or even programming languages have built in functions to find means of big sets of numbers. It's ah, is a pretty easy method to find the center of ah, instead of data we know it's also it's pretty simple. There's only one thing we need to keep track of, um, and if we only have if we need one number to describe where the center of our data is thin, that's perfect. So it's easy and simple, and it really takes into consideration every single data point. Um unlike, say, for example, the median it doesn't take into consideration exactly where the other data points are. It only cares whether they're higher or lower than the median. Now, what are the cons? Well, one downside is that, uh, talking to describe a distribution with just the mean We don't know how spread out it is. We could have, um, a distribution that looks like this and a similar distribution that looks like this. And if they're centered on the same thing, the mean would have no way of telling apart those distributions. Um, so So even though this the central tendency is the same in each, the mean doesn't have a way of distinguishing these distributions. But it goes. It goes the same for the median. In other ways of of finding central tendency, the big one. The big downside of the mean, um is is when we have skewed distributions. That means if we have a distribution that's mostly centered over one bit, but has a couple of of data points that are way out toe one side instead of the mean being where the median would be, it's those points that are out to the side are gonna affect the mean a lot more than the points that are closer and so the mean will be drawn out into the wing of the distribution. This is a problem because now our median and are mean are different things. And we have no. They're two different descriptions of central tendency that are different, and so that discrepancy causes a little bit of trouble. And so that's a major drawback of just using the mean for central tendency. It's a good idea to have the median and the mean, or there's some other way of describing what this distribution looks like.