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Tannin
Can't remember
Joined: 06 Aug 2006 Location: Huon Valley Tasmania
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1061 wrote: | I always thought averages were about sampling a group of people and dividing the result by the number sampled.
In a case were say they sample 100 people find out what each individual earns add it all together then divide by 100 to come at the average wage. Are you telling me that it's not how it is done, if so then it seems to be creative accounting and extremely misleading to me an unedumacated nong! |
In one word, 1061, no.
An "average" is a calculated "central" value of a set of numbers. Because sets of numbers have different properties, there is no one method of calculating the central value; you have to select the most appropriate method according to the particular case. Failing to select an appropriate measure of central tendency ("average") is a mathematical howler, and will guarantee you a fail on any statistics exam.
There are well-established, well-known guidelines for the selection of a suitable method. The arithmetic mean (which is what you just used) is one of these methods, and although quite primitive it works well, but only so long as the mathematical assumptions underlying your calculation are valid. One of these assumptions is that the thing we are measuring the central tendency of is evenly distributed around the centre. (I.e., the left-hand side and the right-hand side of it, if you graph them, are roughly the same shape.)
Using the arithmetic mean as an indication of central tendency on a skewed distribution (i.e., anything where you have a lopsided graph) is a statistical howler on a par with trying to use a hammer and nail to join two sheets of glass together - perfectly good technique, wrong time to use it. Try that in an exam and you'll fail the question every time.
In most cases, the appropriate measure of central tendency ("average") for skewed distributions (like income or retirement age or daily change in a stock price) is the median, though in some instances the mode might be preferred. In other cases again - more typically in engineering rather than the social sciences - you might use the geometric mean or the harmonic mean.
(Note that although it is usually a pretty dumb mistake to mis-measure central tendency of a skewed distribution (such as income) with the arithmetic mean, this is not to say that the mean should not be calculated even so, as it has many other uses in a wide variety of more advanced statistical calculations.) _________________ �Let's eat Grandma.� Commas save lives! |
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Tannin
Can't remember
Joined: 06 Aug 2006 Location: Huon Valley Tasmania
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1061 wrote: | Wouldn't median then be better broken down into percentages as lumping it in with averages seems dishonest. |
The median is an average. _________________ �Let's eat Grandma.� Commas save lives! |
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1061
Joined: 06 Sep 2013
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Then the average wage is an inflated LIE! |
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Tannin
Can't remember
Joined: 06 Aug 2006 Location: Huon Valley Tasmania
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Exactly!
The mean wage (what statistical idiots call the "average" wage) is roughly $72,000, but nearly everyone gets far less than this (around $43,000 is the average). Roughly one quarter get the "average" (arithmetical mean) wage or higher. Roughly three quarters get less. *
In fairness, I should note that the mean wage, though it's a gross abuse of statistical honesty in most contexts, still has some uses so long as its limitations and tendency to mislead are understood. For example, if you are a worker employed by Ford (say), you are probably interested in the correct average wage that Ford workers like you take home, which is the median. This tells you far more about how well off you and most of your fellow employees are than the mean would. If, on the other hand, you are Mr Henry Ford, you probably don't much care about individual workers, you only care about the total payout for all of them (which is the amount you spend). So in your case (as Mr Ford), the mean will probably be more useful. Notice that in this second case, Mr Ford is really interested in the total. He's not really using the mean as an indicator of central tendency, he's using it as a proxy for total cost.
Similarly, Coles cares about the mean spend per shopper. They don't care if they get $50 from lots of people and $500 from a few, or whether they get $150 from everyone, just so long as they get the total they want. As a shopper, though, you probably care about the median spend, as that gives you a far better indication of how big a grocery bill you can expect.
(As a matter of detail, Coles actually goes way further than this: they spend millions of dollars a year on very sophisticated analysis of your shopping habits right down to an individual level, and use that data to target ways to extract more from you. This is why they love their Fly Buys program. They are happy to give a bit of stuff away because the data they extract about you, on average, more than makes up for that small cost. Woolies does the same of course.)
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* Not a precise figure! There are all sorts of assumptions and choices involved in the calculation of this sort of figure. Are we including unemployed people or not? What about part-timers? Are we looking at just wages or all income including benefits, director's fees, self-funded super, interest, rent and dividends? Are we calculating on a per-person or a per-household basis? And so on, endlessly. I've used three-quarters as a reasonable middle ground figure but you can easily find numbers anywhere between two-thirds and four-fifths. As always, the devil is in the detail. _________________ �Let's eat Grandma.� Commas save lives! |
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think positive
Side By Side
Joined: 30 Jun 2005 Location: somewhere
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Tannin wrote: | Exactly!
The mean wage (what statistical idiots call the "average" wage) is roughly $72,000, but nearly everyone gets far less than this (around $43,000 is the average). Roughly one quarter get the "average" (arithmetical mean) wage or higher. Roughly three quarters get less. *
In fairness, I should note that the mean wage, though it's a gross abuse of statistical honesty in most contexts, still has some uses so long as its limitations and tendency to mislead are understood. For example, if you are a worker employed by Ford (say), you are probably interested in the correct average wage that Ford workers like you take home, which is the median. This tells you far more about how well off you and most of your fellow employees are than the mean would. If, on the other hand, you are Mr Henry Ford, you probably don't much care about individual workers, you only care about the total payout for all of them (which is the amount you spend). So in your case (as Mr Ford), the mean will probably be more useful. Notice that in this second case, Mr Ford is really interested in the total. He's not really using the mean as an indicator of central tendency, he's using it as a proxy for total cost.
Similarly, Coles cares about the mean spend per shopper. They don't care if they get $50 from lots of people and $500 from a few, or whether they get $150 from everyone, just so long as they get the total they want. As a shopper, though, you probably care about the median spend, as that gives you a far better indication of how big a grocery bill you can expect.
(As a matter of detail, Coles actually goes way further than this: they spend millions of dollars a year on very sophisticated analysis of your shopping habits right down to an individual level, and use that data to target ways to extract more from you. This is why they love their Fly Buys program. They are happy to give a bit of stuff away because the data they extract about you, on average, more than makes up for that small cost. Woolies does the same of course.)
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* Not a precise figure! There are all sorts of assumptions and choices involved in the calculation of this sort of figure. Are we including unemployed people or not? What about part-timers? Are we looking at just wages or all income including benefits, director's fees, self-funded super, interest, rent and dividends? Are we calculating on a per-person or a per-household basis? And so on, endlessly. I've used three-quarters as a reasonable middle ground figure but you can easily find numbers anywhere between two-thirds and four-fifths. As always, the devil is in the detail. |
Man that fly buys is driving me nuts, every time you swipe your card, you get an email, buy this and get these points, agh, going to block their emails _________________ You cant fix stupid, turns out you cant quarantine it either! |
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Culprit
Joined: 06 Feb 2003 Location: Port Melbourne
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Get the lube out and get prepared to be screwed. This is Rich V Poor now. Australians finally may change their apathetic attitude and actually start jumping up and down.
You cannot run a Country like a business and these clowns think you can. Starving your family for a month so you can scream that you have a budget surplus is just plain stupid.
The LNP will sell everything off to their rich mates to expand their business interests and simply follow the Jeff Kennet plan and those in Victoria are all seeing the ramifications of that. |
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Dark Beanie
Joined: 06 Feb 2004 Location: A galaxy far, far away.
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Yep, once you sell off the farm, very hard to get it back.
Private is not always better. _________________ If you are foolish enough to be contented, don't show it, but just grumble with the rest. - Jerome K Jerome |
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David
I dare you to try
Joined: 27 Jul 2003 Location: Andromeda
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pietillidie
Joined: 07 Jan 2005
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All to satisfy completely fraudulent economic claims, no less.
People ought to be ripping the bastards to shreds over this; the arguments are absolute lies driven by ideological whackos and sadists who think the poor need to be punished for their sins.
There are no unicorns, fairies and bunyips. And there is no budget problem and never has been. Why people would let the apocalyptic David Koreshes of economics set policy for them is beyond me. _________________ In the end the rain comes down, washes clean the streets of a blue sky town.
Help Nick's: http://www.magpies.net/nick/bb/fundraising.htm |
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Jezza
2023 PREMIERS!
Joined: 06 Sep 2010 Location: Ponsford End
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Wokko wrote: | It's like year 9 maths all over again. Mode if I remember is the value that occurs the most. So if more people earned $23,000 than any other value, then that's the Modal Average. Not sure where that's useful but I'm sure it is somewhere. |
More like Year 12 Further Maths again!
Mean = Average
Mode = Most frequent
Median = Middle value _________________ | 1902 | 1903 | 1910 | 1917 | 1919 | 1927 | 1928 | 1929 | 1930 | 1935 | 1936 | 1953 | 1958 | 1990 | 2010 | 2023 | |
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Tannin
Can't remember
Joined: 06 Aug 2006 Location: Huon Valley Tasmania
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Wokko
Come and take it.
Joined: 04 Oct 2005
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What concerns me is that none of these reports tie these cutting back of government and services to less taxes. So far it's looking like the Cadbury block that is suddenly smaller but costs the same.
No point cutting government payments and services while maintaining or raising taxation levels. If people have to pay their own way on things, then government needs to get their hand out of their pants. |
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stui magpie
Prepare for the worst, hope for the best.
Joined: 03 May 2005 Location: In flagrante delicto
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I love all the histrionics over the commission of audit report. People are behaving as though it's recommendations are draft legislation.
Lets wait and see what actually happens in the budget. Most of those recommendations will not get adopted at all, some will be adopted in part.
The whole reason for releasing the recommendations is so Hockey can come out of the budget looking like it could have been a lot worse. _________________ Every dead body on Mt Everest was once a highly motivated person, so maybe just calm the **** down. |
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Tannin
Can't remember
Joined: 06 Aug 2006 Location: Huon Valley Tasmania
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^ Gahh, how gullible are you?
Abbott appointed the "commission", Abbott set the terms, Abbott told it what to consider and when to report, the members are all Liberal Party members or fellow travelers from the same hard-right big business lobby Abbott himself belongs to. Abbott's repeated lie is that "this isn't a report by the government, it's a report to the govermnent", and it's palpable rubbish.
The contents of the report provide a chilling insight into the aims of the Abbott government. _________________ �Let's eat Grandma.� Commas save lives! |
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stui magpie
Prepare for the worst, hope for the best.
Joined: 03 May 2005 Location: In flagrante delicto
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Tannin wrote: | ^ Gahh, how gullible are you?
Abbott appointed the "commission", Abbott set the terms, Abbott told it what to consider and when to report, the members are all Liberal Party members or fellow travelers from the same hard-right big business lobby Abbott himself belongs to.
Abbott's repeated lie is that "this isn't a report by the government, it's a report to the govermnent", and it's rubbish.
The contents of the report provide a chilling insight into the aims of the Abbott government. |
OK. Hold that thought and lets review what's in the budget in 2 weeks against what's in the audit report and we'll see who the gullible one is. _________________ Every dead body on Mt Everest was once a highly motivated person, so maybe just calm the **** down. |
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