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1939

(1,683 posts)

13. One of the reasons

Reply to Donald Ian Rankin (Original post)

Sat May 30, 2015, 09:25 PM

May 2015

Most people get a smattering of statistics in school where they are taught using the Normal/Bell Curve. In the Normal Curve, the mean, median, and mode are all the same. In a skewed distribution like the Log Normal, the mode is always less than the median and the median is always less than the mean.

1. Calculate natural logarithm of each data element (use grouped data for very large data sets).

2. Calculate the mean (mu) and standard deviation (sigma) of the logarithms of the data.

3. Calculate the mean, median, and mode of the log normal curve.

Mean = exp (mu + sigma-squared/2)

Median = exp (mu)

Mode = exp (mu - sigma-squared)

I used to work in reliability and maintainability engineering and log normal was the best fit for repair times, parts order times, or any thing that was bounded by zero at the left end but could go to infinity on the right end. Income would appear to fit that distribution.

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Maths 101: the mean vs the median [View all] Donald Ian Rankin May 2015 OP

Good reminder... cyberswede May 2015 #1

Reading the link reminds me of just how sorry our education system is, or how some folks just Hoyt May 2015 #2

So when Walmart brags that the Average (mean) worker TexasBushwhacker May 2015 #3

That might actually be a situation where the mode is worth looking at. N.T. Donald Ian Rankin May 2015 #4

Indeed TexasBushwhacker May 2015 #6

It depends on the data set Trekologer May 2015 #35

A LOT of people seem to not understand these concepts. MoonRiver May 2015 #5

I'd settle to have many stopping using "loose" in place of "lose." Nuclear Unicorn May 2015 #32

Well that's another discussion. MoonRiver May 2015 #34

Thank you for throwing the mode in at the end Warpy May 2015 #7

Mode doesn't really work for income Recursion May 2015 #15

Think you have an exasperation related typo Moliere May 2015 #8

Thank you. Fixed. Donald Ian Rankin May 2015 #21

One of my pet hates is "XXXXX is growing exponentially". Nye Bevan May 2015 #9

The weakness with that thread isn't the difference between mean vs median. lumberjack_jeff May 2015 #10

Which is why corporations and their fluffers loved NAFTA and are slobbering over the TPP. Ikonoklast May 2015 #43

One of the few things that stuck with me from my Ed. Research class is 'the mean follows the tail' Gidney N Cloyd May 2015 #11

Right, and looking at the median alone can obscure changes in the tail. Gormy Cuss May 2015 #16

The variance is a good clue there Recursion May 2015 #19

It's acceptable so long as that curve is maintained. Gormy Cuss May 2015 #20

I like values at quintiles. Donald Ian Rankin May 2015 #25

True. In principle those are just "expanded medians", if you will Recursion May 2015 #29

But it can still skew the the results, depending on what the middle number is. Exilednight May 2015 #12

One of the reasons 1939 May 2015 #13

No, that's not quite right. Donald Ian Rankin May 2015 #22

Most of the skewed distributions 1939 May 2015 #41

For all practical purposes, sure. Donald Ian Rankin May 2015 #42

For all practical purposes 1939 May 2015 #44

One other thing to add, in something as large and complex as the U.S. economy, it's Exilednight May 2015 #14

Depends on what you mean by income. 1939 May 2015 #45

Several problems arise. Exilednight May 2015 #46

So 1939 May 2015 #47

It's befuddled economists for a very long time. It's not that Exilednight May 2015 #48

lies, damn lies, and statistics. KG May 2015 #17

Bill Gates is volunteering one afternoon at the soup kitchen central scrutinizer May 2015 #18

You've still got typos muriel_volestrangler May 2015 #23

Fixed, I think. Donald Ian Rankin May 2015 #24

That was all that I could see (nt) muriel_volestrangler May 2015 #26

Thank you! I saw that thread myself. I've had the discussion about raccoon May 2015 #27

Plenty of GD posts are mean. joshcryer May 2015 #28

It seems to be the mode of operation here Recursion May 2015 #30

Have you no sense of decency, sir? At long last, have you left no sense of decency? Donald Ian Rankin May 2015 #31

So, what you're saying is -- on average, numbers tend to be mean. Nuclear Unicorn May 2015 #33

They could also be irrational Trekologer May 2015 #36

Well, of course they're irrational. You have to count all just to get sum. Nuclear Unicorn May 2015 #39

So to be useful in comparing what is happening economically hootinholler May 2015 #37

The skew isn't quite that, but it's pretty close. Donald Ian Rankin May 2015 #38

And though you did not explicitly say it (but did imply it) rock May 2015 #40