Rocky Ford enterprise., 1895-08-01
THE FALL OF PRICES.
WHAT ARE THE TRUE FIGURES
IN THE PROBLEM7
Champions of Gold Standard Accused of
Using False Averages-How Mathe-
matieai Accuracy Requires Computs-
tion to BE MadA


matio.l Accuracy Requires Comput.-
tion to BE Mad4
DO. Mason in Chicago Daily Record:
In part the issue between those who
favor the free coinage of silver. OF BIZ
metallism, and those who oppose such
coinage is a question which involves
the extent of the fall of prices since
the year 1873. The silverites aver that
the decline in the prices of commodities
in general exhibits signal proportion
to the decline In the price of silver bull
lion, the downward movement OF the
latter being responsible for the down.
ward movement of the former. To sup
port this view various evidences are
set forth; for instance, that silver Dull
lion has had during its shrinkage OF
valuation in the worlds markets GER
tain steadiness of purchasing power In
exchange for staple articles, while the
purchasing power. Of gold has corre-
spondingly advanced. This position II
rejected by the goldites. who resort to
elaborate statistical tables Of prices for
proof that the contention of their op-
ponents is untrue, and seem to show by
the quoted figures, that the fall of prices
from 1860 to 1892, covering 232 different
| commodities, was only about per cent
on the average, SO that the decline from
1873 was from heavy advance In
prices above what they were in 1860,
and not from a legitimate starting
point.
Now there is an insuperable objection
to the use of these tabulations of aver
age prices. They are not actual prices,
but only theoretic prices, and they bear
the same sort of relation to actual
prices which sophistry bears to legiti-
mate argument. In brief, they are
prices obtained by violating a rule OF
arithmetic, yet they are paraded as
having all the faculties and inclinations
Of mathematical accuracy and certainty,
while really involving an increase OF
blunder at every advancing step OF
their spurious computation or of their
complication with other prices. II, for
example, a fundamental error of arith-
! metical calculation is committed in
| obtaining the average price Of any In
/ dividual commodity for one day, how
much augmented and aggravated must
the error become when the calculation
IL extended over week, a month, or
year, and how utterly unreliable. and
even worthless. must such average
price become when wrought into COM
bination with 231 other average prices,
each arrived at through the same
vicious and misleading process directly
violating arithmetical requirements.
In order to compute an average price
arithmetic demands the division of ag-
gregate cost by aggregate quantity; or,
to express the rule differently, there
must be obtained first of all the total
Of the quantities sold Of any commodity
or of an assortment of commodities,
sum of values realized at the various
prices, whereupon the sum is to be d.
vided by the total, and the quotient
is the average price. But within the
last half century there has come into
vogue bastard system Of calculating
average prices-a method which prob
ably had its origin in the frequent i'm
possibility of procuring the quantities
and the values indispensable to arith-
metical accuracy. By this illegitimate
process the proper and essential data
are entirely, arbitrarily, recklessly ig-
ncssd. and so-cGlled average prices are
computed by adding together the DIFF
ferent prices and dividing by their
numbers-a departure from fact and
truth which is without an atom of rea-
son or justification, because 1t invaria-
bly, leads to error continually, in every
direction whittier 1t proceeds, and ac-
cumulates error upon error until jum-
BILE of absurdities and inconsequentiali-
ties has been put in mathematical form
assailable strength, yet worthless for
any purpose of argument except to
demonstrate its falsity and utter un-
reliability.
Let me here illustrate the wide dif-
ference in result between the genuine
method and the spurious mthod of COM
putting average prices: Ten barrels Of
flour at $3.75 each and one barrel at
$3.50 would amount to $44: dividing
this sum by eleven, which is the total
of quantities, we have 81 as the aver
age price. Or, on reversing the terms
of the problem, one barrel of flour at
$3.75 and ten barrels at $3.50 each
would amout to $6S.75; and, as before.
dividing by IL, we obtain $6.25 as the
average. This is the arithmetical
method-the sound process; 1t will en-
dure every test of accuracy to which 1t
can be subjected. But the bastard
method arrives at exactly the same an
swer in both Of these problems. Ac-
cording to that method the two prices
l-$3.75 and $6.50-are added, making
the sum of $10.25 in each case; and on
division by two, which is the number
Of different prices. we get $5.12k as
the average price-a bastard average
which is $1.12k above the fact in one
instance. and $1.121s below the fact in
the other instance. At the rate above
the fact the eleven barrels would have
cost $56.37&an error Of $12371a-a lit
tie more than 2S per cent wrong. AT
the rate below the fact the eleven bar
rels would have cost precisely the same
as before, with the same amount Of
error, but now too little. Save as
curiosities of maladroit computation
what practical use can such trash oi
statistics be to anybody? To palm them
off upon the public as genuine prices
IT.