The Yale expositor., 1895-07-26
THE FALL OF PRICES.
WHAT ARE THE TRUE FIGURES
IN THE PROBLEM
Cha mpIons of Gold standard Accused OF
Using False Averages Mathe-
NAUTICAL Accuracy Requires Computa-
tIon to he Made.

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 comm odities
in general exhibits a signal proportion
to the declire in the price of silver bull
lion, the downward movement or 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 bull
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 Is
rejected by the goldites. who resort 10
elaborate statistical tables OF prices LOT
proof that the contention OF their OPP
ponents is untrue, and seem TO show Dy
the quoted figures, that the fall OF prices
from 1860 to 1892, covering 2S2 different
commodities, was only about per cent
on the average, so that the decline lroni
1873 was from a heavy advance In
prices above what they were In lSoO'
and rot from 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 pear
the same sort of relation TO actuai
prices which sophistry bears to legltl-
mate argument. In brief, they are
prices obtained by violating rule Oh
arithmetic, yet they are paraded as
having all the faculties and inclinations
of mathematical accuracy and certainty
while really involving an increase oil
blunder at every advancing step oil
their spurious computation or II their
complication with other prices. III, TOT
example. a fundamental error OF arith-
metlcal 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
is extended over a week. a month, or 2
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 di-
vided by the total, and the quotient
is the average price. But within the
last half century there has come into
vogue a 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 10 arith-
metlcal accuracy. BY this illegitimate
process the proper and essential data
are entirely, arbitrarily, recklessly ig-
nored, ard so-callei 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 il invaria.
bly, leads to error continually, in every
direction whittier it proceeds, and ac-
cunulates error upon error until jun
BILE of absurdities and inconsequeItiali-
ties has been put in mathematical form
with the superficial appearance of un-
assailable strength, yet worthless for
any purpose of argument except to
demonstrate its falsity and utter un-
reliability.
Let me here illustrate the wide diff
ference in result between the genuine
method and the spurious mthod of COM
putting average prices: Ten barrels OF
-four at 1915 each and one barrel al
$3.50 would amount to s44; dividing
this sum by eleven, which is the tota
of quantities, we have 81 as the aver
age price. Or, on reversing the terms
of the problem, one barrel of flour al
1918 ard ten barrels at $3.50 each
would amout to $6s.75; and, as before
dividing by IL, we obtain 1925 as the
average. This is the arithmetica
method-the sound process; 1t will en-.
dure every test of accuracy to which II
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 price:
-$3.75 and $6.50-are added. making
the sum of $1025 in each case; and OF
division by two, which Is the number
of different prices, We get S5.12h al
the average price--a bastard average
which is $1.1212 above the fact in ONT
! instance, and S1.l21s below the fact IL
I the other instance. At the rate abov,
the fact the eleven barrels would hav,
cost $56.37kan error of $12.371a-a lit
tie more than % per cent wrong. A
the rate below the fact the eleven bar
rels would have cost precisely the sam,
as before, with the same amount o
error, but now too little. Save al
curiositles of maladroit computation
what practical use can such trash o