Tim Merrigan <
tppm@ca.rr.com> wrote:
BTW according to https://www.usinflationcalculator.com/inflation/current-inflation-rates/
Annual inflation rates over the last ten years were:
2013: 1.5%
2014: 0.8%
2015: 0.7%
2016: 2.1%
2017: 2.1%
2018: 1.9%
2019: 2.3%
2020: 1.4%
2021: 7.0%
2022: 6.5%
2023 to date: 3.7%
For a 10 year mean of 3%, mode of 7%, and median of 2% (if I
calculated the median correctly).
If I assume 2023 -- which is about 5/6 over -- will remain at 3.7%,
then at the end of 2023, the mean will be 2.7%, the mode will be 2.1%,
and the median will be 2.1%.
The mode isn't really meaningful in this context; it's 2.1% only
because that's the only number that appears more than once.
But there are lots of different means. There's a different power mean
for each real number. You raise every element to the Nth power, take
the average, and take the Nth root of the result. Where N=1 you have
the usual average, called the arithmetic mean. N=2 is called the
quadratic mean, or Root-Mean- Square (RMS). The RMS is useful for
measuring AC voltage, as X volts RMS AC has much the same effect
as X volts DC. N=0 (or rather the limit as N approaches 0) is the
geometric mean, so called because the geometric mean of the sides
of a rectangle gives the same area as a square whose sides are the
geometric mean. It's useful for finding the average of an exponential distribution. For instance one minute is the geometric mean of one
second and one hour. N=-1 is the harmonic mean, useful when averaging
speeds. The harmonic mean of your speeds is the constant speed that
would give you the same trip duration. It's also useful in finding
equivalent resistances when you have resistors in parallel.
Then there's the arithmetic-geometric mean (AGM), in which you take
both of those two kinds of means of a pair of numbers, then repeat the
process with the resulting pair of means, ad infinitum. The two means
converge very rapidly. This is useful, not for actually averaging
data, but for rewriting formulas in terms of an AGM to get rapid
convergence. That's how it's possible to calculate trillions of
digits of pi, for instance. If you tried to use one of the simpler
formulas for pi, such as 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...
you'd be lucky to get a dozen digits after weeks on a supercomputer.
"Mode" is the most common value. For some distributions, there are
two or more modes. Or every value is different, so you have to decide
on bin sizes, i.e. make an arbitrary choice of how close values have
to be to be considered equal.
"Median" is the value in the middle once the list is sorted in
numerical order. It's useful if there are outliers. For instance if
Elon Musk were to move to your small town, the average net worth of
its inhabitants would increase enormously.
ObFandom: Someone once humorously suggested that the fairest way to
weigh votes on future Worldcon locations is to average all of the
locations voted for. But it was pointed out that if just one joker
votes for another solar system, even if it's the closest one, and even
if 20,000 people voted for somewhere on Earth, the average would be
well outside our solar system. The median would make more sense here.
Or rather the epicenter of the median, since the median would probably
be deep underground. If the epicenter is in an ocean or other body of
water, the closest point of dry land would be used.
So which kind of mean is best for averaging inflation rates? Assuming
that by "average" you want the constant inflation rate that would have
resulted in the same price increase, then none that I've mentioned
will do. You want to turn them into price ratios by dividing them by
100 and adding 1, i.e. 1.015, 1.008, 1.007, 1.021, 1.021, 1.019, 1.023
1.014, 1.070, 1.065, 1.037, then taking the geometric mean by multiplying
them together to get about 1.34, then taking the 11th root of the result.
Or, equivalently, take the log of 1.34, divide it by 11, then take the
antilog of the result. You'll get 1.027, or 2.7%. That happens to be
close to the arithmetic mean, but it didn't have to be.
A separate issue is that I don't trust any of these official
statistics. I know how my spending has varied, and it has gone up
much more than that (ignoring rent, since I've moved twice since
2013), even though I live increasingly frugally. As for rent, I just
looked up the apartment complex where I lived in 2013, and the lowest
rent for any unit in that complex is 72% more than what I was paying
in 2013. That's more than *twice* the official 34%.
Many of my favorite foods have more than doubled in price since 2013,
even though I'm still living in the same general area and still
shopping in the same stores. Metrorail fares have also more than
doubled, even as Metrorail service has become much worse.
--
Keith F. Lynch -
http://keithlynch.net/
Please see
http://keithlynch.net/email.html before emailing me.
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