Bauhaus-Universität Weimar

Volltext On mean values for direct measurements (2)

Titel:
On mean values for direct measurements
Person:
Scripture, Edward W.
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit28768/20/
```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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