Limit the effects of extreme data observations

How to limit the effects of extreme data observations, and set any z-score less than -3 to -3, and any z-score greater than +3 to +3.

Answer 1

[Paras Gupta]

Hi Pawel,

I understand that you want to limit the effects of extreme data observations using z-scores.

Setting the z-scores less than -3 to -3 and z-scores greater than +3 to +3, we can limit the effects of extreme observations and obtain corresponding adjusted data points that are within the desired range. The following MATLAB code shows how to do the same:

clear;
clc;

% Example dataset
data = [10, 12, 15, 20, 25, 35, 40, 41, 42, 44, 500];

% Calculate mean and standard deviation
meanValue = mean(data);
stdValue = std(data);

% Compute z-scores
zScores = (data - meanValue) / stdValue

zScores = 1×11

-0.4292 -0.4152 -0.3942 -0.3591 -0.3241 -0.2541 -0.2190 -0.2120 -0.2050 -0.1910 3.0030

% Limit extreme z-scores
zScores(zScores < -3) = -3;
zScores(zScores > 3) = 3;

% Apply adjusted z-scores to original data points
adjustedData = meanValue + zScores * stdValue

adjustedData = 1×11

10.0000 12.0000 15.0000 20.0000 25.0000 35.0000 40.0000 41.0000 42.0000 44.0000 499.5716

You can also refer to the following documentation on 'Standardized z-scores' to make use of the inbuilt 'zscore' function.

https://www.mathworks.com/help/stats/zscore.html

Hope this helps.