How to resolve the algorithm Cumulative standard deviation step by step in the J programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Cumulative standard deviation step by step in the J programming language
Table of Contents
Problem Statement
Write a stateful function, class, generator or co-routine that takes a series of floating point numbers, one at a time, and returns the running 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 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,
{ 2 , 4 , 4 , 4 , 5 , 5 , 7 , 9 }
{\displaystyle {2,4,4,4,5,5,7,9}}
, which is
2
{\displaystyle 2}
.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Cumulative standard deviation step by step in the J programming language
Source code in the j programming language
mean=: +/ % #
dev=: - mean
stddevP=: [: %:@mean *:@dev NB. A) 3 equivalent defs for stddevP
stddevP=: [: mean&.:*: dev NB. B) uses Under (&.:) to apply inverse of *: after mean
stddevP=: %:@(mean@:*: - *:@mean) NB. C) sqrt of ((mean of squares) - (square of mean))
stddevP\ 2 4 4 4 5 5 7 9
0 1 0.942809 0.866025 0.979796 1 1.39971 2
of =: @:
sqrt =: %:
sum =: +/
squares=: *:
data =: ]
mean =: sum % #
stddevP=: sqrt of mean of squares of (data-mean)
stddevP\ 2 4 4 4 5 5 7 9
0 1 0.942809 0.866025 0.979796 1 1.39971 2
require'stats'
(%:@:(%~<:)@:# * stddev)\ 2 4 4 4 5 5 7 9
0 1 0.942809 0.866025 0.979796 1 1.39971 2
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