Hi I want to find a outlier data using standard normal distribution

I'm not used to statistics. So If any error in my question, please give me advice.

I have two requirement.

1. I want to make a standard normal distribution using integer list of data like [15, 13, 18, 20, 22, 17, 16, 16, 30, 18, 15, 16]

2. When a new data is coming to list like 32, I want to check that new data is in range of standard normal distribution with in - 1 sigma from mean

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Thanks for reading my question.

CodePudding user response：

As explained on Wikipedia, the standard deviation σ can be computed as:

σ = sqrt(E[X^2] - E[X]^2)

where E is the expected value (mean). The following simple class does just that:

class Statistics {

    int count = 0; // num values so far
    double mean = Double.NaN; // E[X]
    double meanOfSquares = Double.NaN; // E[X^2]

    public void add(final double value) {
        if (count == 0) {
            mean = value;
            meanOfSquares = value  * value;
        } else {
            mean = (mean * count   value) / (count   1);
            meanOfSquares = (meanOfSquares * count   value * value) / (count   1);
        }
        count  ;
    }

    public double getMean() {
        // sum of all values divided by count
        return mean;
    }

    public double getVariance() {
        // σ^2 = E[X^2] - E[X]^2;
        return meanOfSquares - mean * mean;
    }

    public double getStandardDeviation() {
        // variance is square of standard deviance
        return Math.sqrt(getVariance());
    }
}

You can now check whether a value x is within one σ as follows:

Statistics statistics = new Statistics(): 
statistics.add(10); 
statistics.add(12); 

int x = 5; 
double mean = statistics.getMean();
double sigma = statistics.getStandardDeviation();
if (x < mean - sigma || x > mean   sigma) {
    System.out.println(x   " not within one standard deviation");
}