Calculate variablity over specified interval and apply corresponding calculation back to formula

I'm trying to reproduce a calculation I've seen in a paper called variablity. It's defined as follows:

so Xvariability = sqrt((Xn-Xavg)^2) for 1 to n

Xavg needs to be calculated over a regular interval, in this case, a Y interval of 0.5 with a sensor recording X at irregular intervals of Y.

In the example below, what's the best way to calculate Xavg for 0-0.5, 0.5-1.0, 1.0-1.5 and 1.5-2.0, then apply those Xavg values in the Xvariabilty formula back to each original value of X with corresponding Xavg for the correct interval?

%tables
Y = [0;0.0542;0.0801;0.2222;0.3959;0.4572;0.5110;0.5348;0.5712;0.6099;0.6437;0.6799;0.8011;0.8928;0.9590;1.0110;1.13;1.22;1.31;1.43;1.5;1.61;1.73;1.83;1.91;2.0];
X = [118.7000;207.8000;139.6000;176.0000;177.8000;229.3000;242.4000;138.9000;85.7000;140.8000;164.5000;125.4000;189.8000;164.0000;118.4000;211.4000;148.7000;207.8000;119.6000;116.0000;117.8000;129.3000;242.4000;198.9000;285.7000;130.8000];
YX = [Y,X];

Answer 1

[Bhavana Ravirala]

Hi Daniel,

When we apply a logical condition on an array(Y) it will produce logical array, by giving this as an index to another array(X) we will get the corresponding values.

Y = [0;0.0542;0.0801;0.2222;0.3959;0.4572;0.5110;0.5348;0.5712;0.6099;0.6437;0.6799;0.8011;0.8928;0.9590;1.0110;1.13;1.22;1.31;1.43;1.5;1.61;1.73;1.83;1.91;2.0];
X = [118.7000;207.8000;139.6000;176.0000;177.8000;229.3000;242.4000;138.9000;85.7000;140.8000;164.5000;125.4000;189.8000;164.0000;118.4000;211.4000;148.7000;207.8000;119.6000;116.0000;117.8000;129.3000;242.4000;198.9000;285.7000;130.8000];
k= Y<0.5 & Y>=0; % logical array for the values of Y between 0-0.5
l= Y<1 & Y>=0.5; % logical array for the values of Y between 0.5-1
m=Y<1.5 & Y>=1; % logical array for the value of Y between 1-1.5
n=Y<=2 & Y>=1.5; % logical array for the value of Y between 1.5-2
% X(k)-gives the corresponding values of X with respect to Y
% mean(X(K))-gives the average, sum()-gives the sum of elements
% .^2-performs elementwise square operation.
Xvar=sqrt(sum((X(k)-mean(X(k))).^2)+sum((X(l)-mean(X(l))).^2)+sum((X(m)-mean(X(m))).^2)+sum((X(n)-mean(X(n))).^2));

For more information about logical array refer the documentation below:

Find Array Elements That Meet a Condition - MATLAB & Simulink (mathworks.com)

Hope this helps!

[Daniel Goldstein]

Thank you