분산(variance)과 표준편차(standard deviation) 구하기

백터 A=[a_1,a_2,a_3,....a_N)에 대한 분산(V)과 표준편차( $\sigma$ )는 아래와 같이 구한다.

$V(A)=\frac{\sum_{k=1}^{N} a_{k}^{2} }{N} -(\frac{\sum_{k=1}^{N} a_{k}}{N})^2$

$\sigma(A)=\sqrt{V(A)}$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % calculate variance and standard deviation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [variance, S_deviation] = variance(indata) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % indata : input data % var : variance % dev : standard deviation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % calculate average value mvalue = sum(indata)/length(indata); % calculate square average sqmean = sum(indata.^2)/length(indata); % calculate variance vale variance = sqmean - mvalue.^2; % caculate standard deviation S_deviation = sqrt(variance);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% calculate variance and standard deviation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [variance, S_deviation] = variance(indata)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% indata : input data

% var : variance

% dev : standard deviation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% calculate average value

mvalue = sum(indata)/length(indata);

% calculate square average

sqmean = sum(indata.^2)/length(indata);

% calculate variance vale

variance = sqmean - mvalue.^2;

% caculate standard deviation

S_deviation = sqrt(variance);

>> A=[2,5,7,8,2,4,6,7,2,5,6,2]

A =

2 5 7 8 2 4 6 7 2 5 6 2

>> [a,b] = variance(A)

a =

4.5556

b =

2.1344

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Posted by bayron

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