simple-statistics/src/combine_variances.js

import combineMeans from "./combine_means";

/**
 * When combining two lists of values for which one already knows the variances,
 * one does not have to necessary recompute the variance of the combined lists
 * in linear time. They can instead use this function to compute the combined
 * variance by providing the variance, mean & number of values of the first list
 * and the variance, mean & number of values of the second list.
 *
 * @since 3.0.0
 * @param {number} variance1 variance of the first list
 * @param {number} mean1 mean of the first list
 * @param {number} n1 number of items in the first list
 * @param {number} variance2 variance of the second list
 * @param {number} mean2 mean of the second list
 * @param {number} n2 number of items in the second list
 * @returns {number} the combined mean
 *
 * @example
 * combineVariances(14 / 3, 5, 3, 8 / 3, 4, 3); // => 47 / 12
 */
function combineVariances(variance1, mean1, n1, variance2, mean2, n2) {
    const newMean = combineMeans(mean1, n1, mean2, n2);

    return (
        (n1 * (variance1 + Math.pow(mean1 - newMean, 2)) +
            n2 * (variance2 + Math.pow(mean2 - newMean, 2))) /
        (n1 + n2)
    );
}

export default combineVariances;