120 THEORY OF STATISTICS. 
it is useless in the cases cited at the end of § 6 ; the median wage 
cannot be found from the total of the wages-bill, and the total 
of the wages-bill is not known when the median is given.) (c) It 
is sometimes useful as a makeshift, when the observations are so 
given that the calculation of the mean is impossible, owing, e.g., to 
a final indefinite class, as in Table IV. (Chap. VI. § 10). (d) The 
median may sometimes be preferable to the mean, owing to its 
being less affected by abnormally large or small values of the 
variable. The stature of a giant would have no more influence 
on the median stature of a number of men than the stature of 
any other man whose height is only just greater than the median. 
If a number of men enjoy incomes closely clustering round a 
median of £500 a year, the median will be no more affected by 
the addition to the group of a man with the income of £50,000 
than by the addition of a man with an income of £5000, or even 
£600. If observations of any kind are liable to present occasional 
greatly outlying values of this sort (whether real, or due to 
errors or blunders), the median will be more stable and less 
affected by fluctuations of sampling than the arithmetic mean. 
(In general the mean is the less affected.) The point is discussed 
more fully later (Chap. XVIL). (e¢) It may be added that the 
median is, in a certain sense, a particularly real and natural 
form of average, for the object or individual that is the median 
object or individual on any one system of measuring the character 
with which we are concerned will remain the median on any 
other method of measurement which leaves the objects in the 
same relative order. Thus a batch of eggs representing eggs 
of the median price, when prices are reckoned at so much per 
dozen, will remain a batch representing the median price when 
prices are reckoned at so many eggs to the shilling. 
19. The Mode.—The mode is the value of the variable corre- 
sponding to the maximum of the ideal frequency-curve which 
gives the closest possible fit to the actual distribution. 
It is evident that in an ideal symmetrical distribution mean, 
median and mode coincide with the centre of symmetry. If, 
however, the distribution be asymmetrical, as in fig. 22, the three 
forms of average are distinct, #o being the mode, 4/7 the median, 
and JM the mean. Clearly, the mode is an important form of 
average in the cases of skew distributions, though the term is of 
recent introduction (Pearson, ref. 11). It represents the value 
which is most frequent or typical, the value which is in fact the 
fashion (la mode). But a difficulty at once arises on attempting 
to determine this value for such distributions as occur in practice. 
It is no use giving merely the mid-value of the class-interval into 
which the greatest frequency falls, for this is entirely dependent