Standard Deviation definition states:

A quantity expressing by how much the members of a group differ from the mean value for the group.

The logic below calculates the Standard Deviation for the population of values. If the data is being considered a population on its own, we divide by the number of data points, say N. If the data is a sample from a larger population, we divide by one fewer than the number of data points in the sample, n-1. So you can change the formula accordingly.

Ruby code sample:

#sample = Array[1,2,3,4,5,6,7,8]
sample = Array[1,2,3,4,5]

def calc_standard_deviation(values)
    avg = values.sum {|x| x.to_f} / values.size.to_f
    Math.sqrt(values.sum {|x| (x.to_f - avg.to_f) ** 2} / values.size)
end

puts "Standard Deviation is: " + calc_standard_deviation(sample).to_s

Run the Ruby code to test as below in VS Code:

PS C:\code\Ruby test> ruby .\stdDev.rb
#Ruby Output: Standard Deviation is: 1.4142135623730951

C# code sample:

static void Main(string[] args)
{
	//double[] sample = new double[8] { 1, 2, 3, 4, 5, 6, 7, 8 };
	double[] sample = new double[5] { 1, 2, 3, 4, 5 };

	Console.WriteLine("Standard Deviation is: " + StdDev(sample));
}

public static double StdDev(IEnumerable<double> values)
{
	// Get the mean.
	double mean = values.Sum() / values.Count();

	// Get the sum of the squares of the differences
	// between the values and the mean.
	var squares_query =
					from double value in values
					select (value - mean) * (value - mean);
	double sum_of_squares = squares_query.Sum();

	return Math.Sqrt(sum_of_squares / values.Count());
}

C# Output: Standard Deviation is: 1.4142135623731