tag:blogger.com,1999:blog-5737450142880120395.post1465307898908352111..comments2017-09-11T11:34:27.732-07:00Comments on Economystified: Median vs MeanEconomystifiedhttp://www.blogger.com/profile/13721219444051369880noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5737450142880120395.post-27451566655412894912014-06-11T07:53:07.652-07:002014-06-11T07:53:07.652-07:00And statistics is a lot more than parameter estima...And statistics is a lot more than parameter estimates, like taking the mean, by the way. Opposed to your bit about statistics being 'the art of summarizing numbers' (ehhhhh), I'd say it is more 'the science of figuring out how to answer questions with data'. A lot of what real statisticians do is inventing new methods to test hypotheses and figuring out how to deal with the various biases of different data-types.David Bapsthttps://www.blogger.com/profile/17606476387441191531noreply@blogger.comtag:blogger.com,1999:blog-5737450142880120395.post-34552052928918647912014-06-11T07:49:10.815-07:002014-06-11T07:49:10.815-07:00You appear to have a typo in your 'Rule of Thu...You appear to have a typo in your 'Rule of Thumb' section... both lines refer to the mean. ;p<br /><br />So, yes... you are correct to say there's no hard rules in statistics. Statistics is like a big toolbox, and which one makes sense depends on the question you want to answer and the data at hand.<br /><br />However, the thing to take away is that the mean and the median often don't tell a whole story together. They are two minor tools in the toolbox: if the mean and median are really disparate, it could mean all sorts of crazy things about your data, like maybe its multi-modal or maybe its really skewed. You need other tools in the toolbox to start to differentiate those things.<br /><br />Furthermore, the arithmetic mean (BTW there's a multiplicative mean) is grounded strongly to our understanding of normal distributions, and our typical assumption that datasets of many types conform to that distribution. Central tendencies can be misleading if, for example, your data is unfiromly distributed).<br /><br />Which is the really key thing: the tools in the statistical toolbox don't work without their batteries, and their power source is ASSUMPTIONS. You can't say squat if you aren't willing to say something about the numbers beyond that, yep, those are the numbers there... <br /><br />Taking the mean implicitly assumes that your data is a random sample of an infinite amount of data with a distribution that looks normal-ish and isn't skewed and is unimodal and not bound strongly at zero or anything like that. And maybe those are fine assumptions and maybe they aren't. The median makes fewer assumptions (it has more in common with so-called 'non-parametric' statistics) which is why its useful, but the why and the how and when each is most useful is really up to the user. Ultimately, statistics is more like philosophy and logic than it is like math.David Bapsthttps://www.blogger.com/profile/17606476387441191531noreply@blogger.com