'When would you use the geometric mean?' blog discussion.
Comments

You would use the geometric mean when you want to make inflation seem smaller.
For example  basket of goods:
Good A: 1p
Good B: 10p
Good C: £1
They go up by a penny.
Good A: 200%
Good B: 10%
Good C: 1%
Arithmetric mean: 73.3%
Geometric mean: 30.5%
On the assumption you buy 100 of A, 10 of B, and 1 of C, your old basket cost you £3, your new basket costs you £2+£1.10+£1.01=£4.11 which is 37% more money.
The rest of the article is a bit garbled. What the "not buying naffcaff" anymore but getting supermarket own brand is called is "substitution". This has nothing to do with arithmetric mean  it's a manual adjustment.
There is also a "my model of mobile has more ringtones this year" adjustment to the inflation figures. This is called hedonic (as in pleasure) adjustment. Since you are getting more pleasure out of this phone, but it hasn't changed in price  then it must be cheaper (as you're getting more features for the price). This again is a manual adjustment.
So, to run through the adjustments:
If naffcaff goes up in price, it is assumed that you will buy Poundland's "Floorscrapings of somewhere which sells nice coffee"  since that is poorer quality, and therefore cheaper, your basket of goods is cheaper, so inflation is low. This is the substitution adjustment.
If your mobile stays the same price (or has a small increase) but they loaded it with more games/ringtones  then someone at (I think it's National Statistics these days, but it could be the Treasury) gives a value to those extra features, and says that phone actually fell by that amount of money (despite you not being able to buy it at that price).
So: To recap.
If you buy something which is poorer quality, inflation goes down.
If you buy something which has better quality, inflation goes down.
If you calculate using the new geometric mean, inflation goes down.
Are there any questions?"Follow the money!"  Deepthroat (AKA William Mark Felt Sr  Associate Director of the FBI)
"We were born and raised in a summer haze." Adele 'Someone like you.'
"Blowing your mind, 'cause you know what you'll find, when you're looking for things in the sky." OMD 'Julia's Song'0 
Are they calculating the Geometric Mean of the prices or the change in prices?
If they are using the geometric mean of the changes in prices to come up with an 'average' change in price then that makes some sense. Just taking the geometric mean of a random series of numbers (that are not multiplicative) would not in anyway be meaningful (as demonstrated above).
[I take some issue with some of the comments above. Just because a particular method reduces the statement of inflation or is complicated does not make it necessarily bad or disingenious. I kind of expect the ONS to use appropriate statistical methods that are not easily understood by the man in the street. My degree is in Maths and Stats and I work as a Math teacher but I am comfortable that the guys there use methods that I don't fully understand.]0 
Not particularly relevant to inflation or investments (for which I think artumi_richard has hit the nail on the head), but one way of looking at the geometric mean is the average order of magnitude (which follows from my post #3 above).0

[I take some issue with some of the comments above. Just because a particular method reduces the statement of inflation or is complicated does not make it necessarily bad or disingenious. I kind of expect the ONS to use appropriate statistical methods that are not easily understood by the man in the street.
My issue with the change, is that it is a change. They've used arithmetric mean, now they're using geometric mean. The two can't be compared because (surprise, surprise) they're different.
No matter which you "approve of", it means the ONS are going to be/have been wrong for a number of years simply because both methods can't be right. Both methods could be wrong.
Is the Government going to backcalculate through the years and readjust the price index using the new method? Sure...
As for disingenuous, some people think so.My degree is in Maths and Stats and I work as a Math teacher but I am comfortable that the guys there use methods that I don't fully understand.]
That's just an Appeal to Authority. You should be making everyone demonstrate the truth and validity of their methods. If you don't understand, then ask. The alternatives is taking the words of our "betters" unchallenged, along with tugging the forelock and smelling the glove."Follow the money!"  Deepthroat (AKA William Mark Felt Sr  Associate Director of the FBI)
"We were born and raised in a summer haze." Adele 'Someone like you.'
"Blowing your mind, 'cause you know what you'll find, when you're looking for things in the sky." OMD 'Julia's Song'0 
Old_Wrinkly wrote: »Are we talking speed (undirectional scalar quantity) or the directional vector 'velocity'?
If I understand the difference between speed and velocity correctly, then the overall velocity is zero, as the rabbit is back where he / she started! That's not the answer I was driving at!
To rephrase the question slightly: suppose I ran a certain distance at 4 mph, and then ran the same distance again at 2 mph. Over the whole journey, what is my overall average speed?"Peter Pan is 2. Shirley Bassey is 3. Dr Ian Paisley is 4. King Lear is 5. Why?"
"...also known as taking in the Spanish Cub Scout leader. (Cryptic) (5)"
Thanks to MSE, I've seen Citizen Kane, 2001: A Space Odyssey and Serenity for FREE!0 
I meant speed.
If I understand the difference between speed and velocity correctly, then the overall velocity is zero, as the rabbit is back where he / she started! That's not the answer I was driving at!
To rephrase the question slightly: suppose I ran a certain distance at 4 mph, and then ran the same distance again at 2 mph. Over the whole journey, what is my overall average speed?
Strangly I was thinking about a problem yesterday and the answer to this question sums it up! I reckon the answer is 2.6667mph.
the reason is to do with what you take as the base of your average. ie time or distance.
So if you take teh distance you run as 1 mile. 4mph for one mile takes 0.25 hours (15 mins) then you run back at 2mph and it takes 0.5 hrs (30mins). So you ran at 4mph for 0.25hrs and 2mph for 0.5hrs. Total time 0.75 hours. You covered 2 miles so 2 / 0.75 = 0.266667.
well thats my answer anyway.
My own personal problem of consideration was that my car gives me an average speed travelled for the journey (mph) as well as an average fuel consumption (mpg). It made me think, do they calculate them based on how long your driving for or how far you are driving. if it was distance based then, the number of miles would appear in the calculation twice so the answer for say average speed would be meausured in per hours not miles per hour.
Or am I just overworked and confused myself!?Here to help and be helped!
New to MB, running profit, £16 from MB, £30 cashback!0 
My issue with the change, is that it is a change. They've used arithmetric mean, now they're using geometric mean. The two can't be compared because (surprise, surprise) they're different.
No matter which you "approve of", it means the ONS are going to be/have been wrong for a number of years simply because both methods can't be right. Both methods could be wrong.
Is the Government going to backcalculate through the years and readjust the price index using the new method? Sure...
As for disingenuous, some people think so.
Well they have changed the name from RPI to CPI to demonstrate a change and it could be that one is better than the other. After all none of them are right by definition. They are trying to approximate a number that cannot be calculated exactly. They have changed their method to make it a better approximation to the change in prices.That's just an Appeal to Authority. You should be making everyone demonstrate the truth and validity of their methods. If you don't understand, then ask. The alternatives is taking the words of our "betters" unchallenged, along with tugging the forelock and smelling the glove.
Wow  you're rude(!) and you significantly misunderstood my point. I agree that everybody should be made to demonstrate the validity of their methodology but I am questioning whether everybody can understand the response. I happen to expect that somebody working at the ONS who has spent their whole career working in statistics has an understanding that is deeper and better than mine and that it might take another statistician with greater knowledge and understanding than me to dialogue with them about the suitability of their approach. This is exactly what does go on within the profession. Sometimes I get really bothered that everybody expects to be an expert at everything with just a quick glance over a topic and fully expects to be able to critique a topic they know and understand very little about.0 
My own personal problem of consideration was that my car gives me an average speed travelled for the journey (mph) as well as an average fuel consumption (mpg). It made me think, do they calculate them based on how long your driving for or how far you are driving. if it was distance based then, the number of miles would appear in the calculation twice so the answer for say average speed would be meausured in per hours not miles per hour.
Or am I just overworked and confused myself!?
It gives average speed for the journey in miles per hour and average fuel consumption (presumably for the journey  that's what ours does) in miles per gallon.
So if you travel 80 miles in 1 hour and use 2 gallons of petrol, you'll get an average speed of 80 mph and an average consumption of 40 mpg.
It's distance based in as much as distance appears in the calculation. It appears in each calculation once.0 
View wikipedia page, scroll to bottom, see external link "When to use the geometric mean", visit:
http://www.math.toronto.edu/mathnet/questionCorner/geomean.html
The first example looks like a good use?0 
Strangly I was thinking about a problem yesterday and the answer to this question sums it up! I reckon the answer is 2.6667mph.
the reason is to do with what you take as the base of your average. ie time or distance.
So if you take teh distance you run as 1 mile. 4mph for one mile takes 0.25 hours (15 mins) then you run back at 2mph and it takes 0.5 hrs (30mins). So you ran at 4mph for 0.25hrs and 2mph for 0.5hrs. Total time 0.75 hours. You covered 2 miles so 2 / 0.75 = 0.266667.
well thats my answer anyway.
That's my answer as well. :beer:"Peter Pan is 2. Shirley Bassey is 3. Dr Ian Paisley is 4. King Lear is 5. Why?"
"...also known as taking in the Spanish Cub Scout leader. (Cryptic) (5)"
Thanks to MSE, I've seen Citizen Kane, 2001: A Space Odyssey and Serenity for FREE!0
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