Bauhaus-Universität Weimar

20 
JE. W. Scripture, 
x„ xm 
2P==r 2P=ZS 
Xm », 
and r + s=[jt 
or r=s= 
& 
The relation between Mand xm can be determined by Bernoulli’s 
theorem. When /j. is large, 
M=xm±yr\/ - (18) 
ß 
with a probability of 
7 
P= j— f?-'2 (It + 
V 7T«-' 
0 
The values of y are to be determined from the usual table for 
r 
Computation of the median. The median is defined as that value 
which occupies the position given by 
X° + X°+ . . . +£Cb0 + 1_W + 1 
2 — 2 
in the series of values x„ æa, . . ., xn taken in order of size from 
the smallest to the largest and from the largest to the smallest. 
Let the number of occurrences of each value of x be denoted by 
ma, mh, . . ., m,. The series of differing values x„ x„ . . ., x„ 
finitely expressed, can be regarded as having arisen from the series 
x,, x,, . . ., x„ expressed each to an infinite number of decimals 
by rounding-off all the decimals to the a place. In the a place the. 
set æ, x„ . . ., xa will all agree and can be expressed by m„ xa. 
Likewise we have the sets mb xh, . . ., mr xr. 
When these sets are arranged in order of size 
»1, xa, m,, xb...... m,_, x,_u m, x„ m,+1 xw, . . ., m, x, 
the set containing the median will be mt xt where 
(ma + mb+ . . . +m,_,) — (mH.1+ml+i+ . . . +mr) 
    

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