FALLACIES 143

There are many examples of this dual nature in statistics
whenever politics come into the question. For instance, under
the present British electoral system, it is possible for Party 4
to hold more seats in Parliament than does Party B and yet,
because of the system of electing members, to have a smaller
aggregate of actual votes. It is obvious that if Party 4 are
preparing statistics they will omit all reference to the aggre-
gate number of votes, whereas Party B would lay heavy
stress upon that figure.

Another set of numbers which require close attention
are those expressed as percentages of others. It may sound
childish to say that a number will be equivalent to different
percentages of different numbers, yet it is a common error for
these to become confused. For example, the profit obtained
from the sale of an object is a certain percentage of its cost
price but a totally different percentage of its selling price,
because the selling price also includes the profit. To express
the profit as a percentage of the selling price therefore gives
quite a false impression of the true facts.

Other misconceptions arise in calculating cost or selling
price if one of these prices and the rate of profit are known.
If the cost price is £100 and the profit is 25 per cent. on cost
price, then the selling price is £100+£25=/,125. That is,
to obtain the selling price we add a quarter of the cost price.
If, however, we start with the selling price, we cannot deduct
a quarter of the latter in order to arrive at the cost price. We
have to bear in mind that the selling price of £125is equiva-
lent to cost price plus profit; that is, it is one-and-a-quarter
times the cost price, and we have to deduct only one-fifth:

£125—L25=£100
Percentages are also very misleading in connexion with
the declaration of companies’ dividends in the allocation of
trading profits. The unwary investor who hears that certain
shares are yielding 50 per cent. dividends may think that
if he invests £ 100 in those shares, then in two years he should
be able to double his capital. What has to be remembered,

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