HE THEORY OF STATISTICS. 
agricultural labourers in 38 rural unions. The values (earnings) 
are first of all totalled and the total divided by XN to give the 
arithmetic mean M, viz. 15s. 1119d., or 15s. 11d. to the nearest 
penny. The earnings being estimates, it is not necessary to take 
the average to any higher degree of accuracy. Having found 
the mean, the difference of each observation from the mean is 
next written down as in col. 3, one penny being taken as the 
unit : the signs are not entered, as they are not wanted, but the 
work should be checked by totalling the positive and negative 
differences separately. [The positive total is 300 and the 
negative 290, thus checking the value for the mean, viz. 15s. 
11d. +10/38.] 
Finally, each difference is squared, and the squares entered in 
col. 4,—tables of squares are useful for such work if any of the 
differences to be squared are large (see list of Tables, p. 356). 
The sum of the squares is 16,018. Treating the value taken for 
the mean as sensibly accurate, we have— 
16018 
DL ESS . 
Fix Sn =421'5 
o = 205d. 
If we wish to be more precise we can reduce to the true mean 
by the use of equation (4), as follows :— 
2 16,018 mis 
Fe =4215263 
10 
d=—==02632; d2= 00693 
38 
Hence ol=s2—d?=4214570 
o= 20'529d. 
Evidently this reduction, in the given case, is unnecessary, 
illustrating the fact mentioned at the end of § 4, that small 
errors in the mean have little effect on the value found for the 
standard deviation. The first value is correct within a very 
small fraction of a penny. 
50