The average is a simple term with several meanings. The type of average to use depends on whether you’re adding, multiplying, grouping or dividing work among the items in your set.
This is a companion discussion topic for the original entry at http://betterexplained.com/articles/how-to-analyze-data-using-the-average/
When I was in school I crammed these formulas to pass the exam because no teacher would satisfy my curiosity behind the why, what & how of it. My math teacher would try to explain it to me but his jargon was most of the time out of comprehension… My dad later helped me grasp the stuff.
But I must say you did a superb job of putting the concept in a super easy language and indeed there is no one else could have better explained!
I wish there were more teachers like you… God bless you!
“Let’s say you weigh 160 lbs, and are in an elevator with a 100lb kid and 350lb walrus. What’s the average weight?”
“In this case, we’d swap in three people weighing 200 lbs each [(150 + 100 + 350)/3], and nobody would be the wiser.”
In the first part I quoted, you put the wrong number in. Just thought I’d be nitpicky.
That’s an interesting way to think about the average; I guess I always knew about that, but I’d never explicitly thought about the average being “replace everything with identical things”.
I love your articles; always make me think about things in a different way.
@Prateek: Wow, thanks for the kind words! Glad you are finding the site useful. I’m glad your dad was able to help you out – sometimes you just need to get things from a different viewpoint.
Unfortunately, math is one of those subjects where topics get one (and only one) explanation, and you’re off to the next one.
@Zac: Happy you’re enjoying the site – I fixed up the typo [I had actually put in my own weight instead of the hypothetical numbers which are easier to add up ].
Yeah, it’s amazing how many things we’ve “learned” in the past but haven’t seen from all angles (there’s a few other cool interpretations of the average but I didn’t want the post to be too long). Glad you’re enjoying the articles.
That my friend is one very well put together article! Thank you for the effort taken to show to us ‘simple’ people, how fun math can be, esp; statistics!
Now if you can just get the fudge heads at Oracle and Microsoft to introduce this into their ‘superior’ databases, we will all have much more straight forward lives indeed
This will come in handy for math homework, cause math is my absolute WORST subject. lol…
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This is absolutely brilliant! Knowledge is kind of like comedy. You’ve got to have delivery. If the delivery sucks the response will probably not be very good either. This my friend was fabulous! I would love to study under an individual such as yourself.
Quite delightful and informative. You do the world a service by contributing to a global increase in knowledge of mathematics.
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Informative, Concise, what other everyday uses do you have for old school stat info? How about some information about how we can use calculus in everyday life?
@mrhassell: Thanks, glad you found it useful! The funny thing is I’m one of those simple people too – I want things to be simple and clear instead of rigorous and opaque. Unfortunately, I’m pretty powerless to influence the db designers :).
@kat: Cool, hope it comes in handy.
@Dave: Appreciate the comment, and I totally agree – any subject can be interesting if presented in the right way. I’ll keep cranking out the “aha!” moments as they happen :).
@Chris: Thanks, glad you found it useful. Yeah, one of the great things about blogging is that everyone can add a bit of information into the world.
@NebulousMaker: Thanks, a series on calculus is on the way. It’s a tricky subject to cover with real, everyday applications (i.e., non-physics), but they’re definitely out there.
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A couple more things I noticed after a (second? third? fourth? millionth? I lost count) readthrough (sorry in advance if I’m too notpicky):
“The average is the value that can replace every existing item, and have the same result.” That doesn’t quite apply for the mode or median; for the rest it works, but the median and mode are different ideas entirely. They have their uses, yes, but they don’t fit under that definition of the average.
This might be nitpicky, but I don’t really see where this is analysing data using the average. It shows how to find the average and explains why that works, but it doesn’t really say anything about using that to analyze the data. To me, analyzing data has more to do with variance and the standard deviation, but that might just be me. Maybe I just don’t see it.
Also, here’s something else, possibly more useful for the average, though maybe a little too in depth for this article. The median works to eliminate outliers, but it’s more effective (though more time consuming) to find the mean AFTER eliminating the outliers. Gives a better indicator of what the average really is.
Just a few thoughts on the article and possibly something to put in another article (if I’m too nitpicky, just tell me).
Hi Zac, no worries at all, I like hearing what works and what doesn’t for each article – it’s a good way to improve.
Yeah, on second thought the title may be misleading – it’s more about “understanding the types of averages, with examples” vs “data analysis”, which probably deserves its own follow-up article. The idea of throwing away the outliers is a good one, and helps clean up data that may otherwise be skewed.
I had a similar inkling about the term “average” being applied to the median and mode – hopefully it’s clear that those items aren’t really “averages” so a replacement doesn’t work. But I’ll think about ways to clarify the sentence.
Excellent post. I tried doing a similar explanation a few months ago, so I have a real appreciation for your(better)work.