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Cumulative standard deviation: Difference between revisions
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{{task|Probability and statistics}}
Write a stateful function, class, generator or coroutine that takes a series of floating point numbers, ''one at a time'', and returns the running [[wp:Standard Deviation|standard deviation]] of the series.
The task implementation should use the most natural programming style of those listed for the function in the implementation language; the task ''must'' state which is being used. Do not apply [[wp:Bessel's correction|Bessel's correction]]; the returned standard deviation should always be computed as if the sample seen so far is the entire population.
Use this to compute the standard deviation of this demonstration set, <math>\{2, 4, 4, 4, 5, 5, 7, 9\}</math>, which is <math>2</math>.
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Put_Line ("Deviation" & Float'Image (Deviation (Data)));
end Test_Deviation;</lang>
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<pre>
Deviation 2.00000E+00</pre>
=={{header|ALGOL 68}}==
{{trans|C}}
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printf(($"standard dev := "g(0,6)l$, sd))
)</lang>
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<pre>
standard dev := 2.000000
</pre>
{{trans|python}}▼
▲{{trans|python}}
{{works with|ALGOL 68|Standard - no extensions to language used}}
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}}
<!-- {{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8.8d.fc9.i386]}} -->
A code sample in an object oriented style:
<lang Algol68>MODE STAT = STRUCT(
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printf(($"variance = "g(0,6)l$, (variance OF class stat)(stat)));
printf(($"count = "g(0,6)l$, (count OF class stat)(stat)))
)</lang>
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<pre>
standard deviation operator = 2.000000
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count = 8.000000
</pre>
{{trans|python}}▼
▲{{trans|python}}
{{works with|ALGOL 68|Standard - no extensions to language used}}
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}}
<!-- {{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8.8d.fc9.i386]}} -->
A simple - but "unpackaged" - code example, useful if the standard deviation is required on only one set of concurrent data:
<lang Algol68>LONG REAL sum, sum2;
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LONG REAL value = values[i];
printf(($2(xg(0,6))l$, value, sd(value)))
OD</lang>
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<pre>
2.000000 .000000
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}
</lang>
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<pre>
2 0
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9 2
</pre>
=={{header|Axiom}}==
We implement a domain with dependent type T with the operation + and identity 0:<lang Axiom>)abbrev package TESTD TestDomain
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list(i%) = n
= SQR(MOD(list())^2/i% - (SUM(list())/i%)^2)</lang>
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<pre>
Value = 2, running SD = 0
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</lang>
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<pre>
Values: 2
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</lang>
Execute: ^Q StandardDeviation.Do 2 4 4 4 5 5 7 9 ~<br/>
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<pre>
1 :> 0.0
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}
}</lang>
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<pre>0.000000e+00
1.000000e+00
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=={{header|E}}==
This implementation produces two (function) objects sharing state.
It is idiomatic in E to separate input from output (read from write)
rather than combining them into one object.
The algorithm is {{trans|Perl}} and the results were checked against [[#Python]].
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}
}</lang>
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<pre>
0
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}</lang>
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<pre>running std.dev.: 0
running std.dev.: 1
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}
end</lang>
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stddev (so far) := 1.0
stddev (so far) := 0.9428090415820626
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WScript.Echo(stddev.join(', ');</lang>
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<pre>0, 1, 0.942809041582063, 0.866025403784439, 0.979795897113273, 1, 1.39970842444753, 2</pre>
=={{header|jq}}==
====Observations from a file or array====
We first define a filter, "simulate", that, if given a file of
observations, will emit the standard deviations of the observations
seen so far.
The current state is stored in a JSON object, with this structure:
{ "n": _, "ssd": _, "mean": _ }
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for value in [2,4,4,4,5,5,7,9]:
echo value, " ", formatFloat(sd(value), precision = 0)</lang>
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<pre>
2 0
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Printf.printf "\nStandard deviation: %g\n" (stddev l)</lang>
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<pre>
List: 2 4 4 4 5 5 7 9
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(for N (2.0 4.0 4.0 4.0 5.0 5.0 7.0 9.0)
(prinl (format N *Scl) " -> " (format (Fun N) *Scl)) ) )</lang>
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<pre>2.00 -> 0.00
4.00 -> 1.00
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=={{header|PowerShell}}==
This implementation takes the form of an advanced function
which can act like a cmdlet and receive input from the pipeline.
<lang powershell>function Get-StandardDeviation {
begin {
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EndDataSection</lang>
{{out}}
<pre>
0.0000000000
1.0000000000
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1.3997084244
2.0000000000
</pre>
=={{header|Python}}==
===Using a function with attached properties===
The program should work with Python 2.x and 3.x,
although the output would not be a tuple in 3.x
<lang python>>>> from math import sqrt
>>> def sd(x):
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do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k; g=.5*(g+x/g); end
numeric digits d; return g/1</lang>
<pre>
item 1: 2 average= 2 standard deviation= 0
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var n sd /*mean*/;
run;
</lang>
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<pre>
N SD
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}
var aa = stdDev()</lang>
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<pre>
value 2 SD = 0.0
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}
puts "the standard deviation is: $sd"</lang>
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<pre>the standard deviation is: 2.0</pre>
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End Sub</lang>
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<pre>
0
1
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1.39970842444753
2
</pre>
=={{header|XPL0}}==
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]</lang>
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<pre>
0.00000 1.00000 0.94281 0.86603 0.97980 1.00000 1.39971 2.00000
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}.fp1(L())
}</lang>
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<pre>
zkl: T(2,4,4,4,5,5,7,9).pump(Void,sdf())
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