# Normalize data so that the sum of squares = 1

In presenting geochemical data, I would like to try a statistical method that presents the data in an ISOCON diagram. This method requires scaling all the data to be the same distance from the origin (i.e., normalizing so that the sums of squares = 1). Result: all data points lie along an arc of a circle centered on the origin.

In other words, data points (elements) are scaled down in such a way that the squared sum of values for altered (y-axis) and unaltered (x-axis) rock become unity, allowing the elements to plot along an arc of a circle centered on the origin at a uniform distance of 1 unit.

Would anyone be helpful in explaining what it would mean and necessary steps to normalize my data so that the sum of squares = 1? This will be used on an x-y scatterplot. Which software would process this type of operation best?

So far, I've calculated for each element for both the x-axis (unaltered) and y-axis (altered) material.

1. mean;
2. degrees of freedom;
3. sum of squared errors;
4. variance; and
5. standard deviation.

It's not entirely clear to me what step you struggle with. But for the sake of explanation, assume you have data $x_i, i=1...N$ and you want to compute the normalized data $y_i, i=1...N$ from the $x_i$. Then $$y_i = \frac{x_i}{\sqrt{\sum_{j=1}^N x_j^2}}.$$ The denominator is of course the same for every $i$, so you only have to compute it once.