4 ms·

How To Analyze Data Using the Average

21 points by brett 19y ago

graywh 19y ago
Poor title, but great descriptions and examples. Bonus for harmonic mean.
- kalid 19y ago
  Cool, glad you liked the article. Yeah, I'm still working on the zen of making catchy "click me now!" titles :).
  - yters 19y ago
    I like the aim of your blog. I've noticed that in all subjects there are a few key ideas that everything revolves around, plus a few key results from these ideas. For some reason, the subjects are not organized around those points. School would be so much easier and interesting if the subjects were organized better. I think the bad organization is a consequence of school performance being measured by tests. It is much easier and quicker to merely memorize the formula and regurgitate than to really understand what is going on. Then the people who learned by parroting become teachers and are even less able to explain the crucial principles; resulting in a vicious cycle.
    - kalid 19y ago
      Thanks, glad you like the site. I completely agree -- many ideas can be boiled down to a few key concepts, yet most of the time we're taught to plug and chug (and inevitably forget). It surprsies me how often "cram and forget" is the operating mode for education (I had my share of that). Yep, I think measuring performace with tests is a big part of it. You hit the nail on the head about student interest as well. Many people end up hating math because it is often taught in that rote, formulaic manner.
ejs 19y ago
Interesting discussion, but I think the average is more usefully thought of as the best unbiased predictor. In other words, given no other information about the process the mean is the best prediction one can make.
- kalid 19y ago
  Yeah, there's lots of different interpretations for the average. The predictive one works well (expected value), another one is where the "balancing point" would be if you had physical weights at those coordinates. If you had 1kg weights at distances 2 3 and 10 (sum of 15), you should put the fulcrum of a lever at 5 to keep the set balanced. (Torque on right: 10 - 5 = 5. Torque on left: 5 - 2 = 3, and 5 - 3 = 2, for a total of 5). Different sized masses? You literally take the weighted average :).
- graywh 19y ago
  Any statistician would tell you the mean is biased and the median is less biased.

21 points by brett 19y ago

graywh 19y ago

Poor title, but great descriptions and examples. Bonus for harmonic mean.

kalid 19y ago
Cool, glad you liked the article. Yeah, I'm still working on the zen of making catchy "click me now!" titles :).
- yters 19y ago
  I like the aim of your blog. I've noticed that in all subjects there are a few key ideas that everything revolves around, plus a few key results from these ideas. For some reason, the subjects are not organized around those points. School would be so much easier and interesting if the subjects were organized better. I think the bad organization is a consequence of school performance being measured by tests. It is much easier and quicker to merely memorize the formula and regurgitate than to really understand what is going on. Then the people who learned by parroting become teachers and are even less able to explain the crucial principles; resulting in a vicious cycle.
  - kalid 19y ago
    Thanks, glad you like the site. I completely agree -- many ideas can be boiled down to a few key concepts, yet most of the time we're taught to plug and chug (and inevitably forget). It surprsies me how often "cram and forget" is the operating mode for education (I had my share of that). Yep, I think measuring performace with tests is a big part of it. You hit the nail on the head about student interest as well. Many people end up hating math because it is often taught in that rote, formulaic manner.

ejs 19y ago

Interesting discussion, but I think the average is more usefully thought of as the best unbiased predictor. In other words, given no other information about the process the mean is the best prediction one can make.

kalid 19y ago
Yeah, there's lots of different interpretations for the average. The predictive one works well (expected value), another one is where the "balancing point" would be if you had physical weights at those coordinates. If you had 1kg weights at distances 2 3 and 10 (sum of 15), you should put the fulcrum of a lever at 5 to keep the set balanced. (Torque on right: 10 - 5 = 5. Torque on left: 5 - 2 = 3, and 5 - 3 = 2, for a total of 5). Different sized masses? You literally take the weighted average :).
graywh 19y ago
Any statistician would tell you the mean is biased and the median is less biased.