not entirely sure i got the math spot on, and I'm fairly sure I can do this with a logarithm if I thought hard enough but...

cassidoo_jun_29_2006.js

function meanBits(n) {
    let bits = 1, counted = 0, sum = 0;
    while(counted < n) {
        const depth = Math.pow(2, Math.max(1, bits - 1));
        const count = Math.min(n - counted, depth);
        
        sum += count * bits;
        counted += count;
        bits++;
    }
    return Math.round(sum / n);
}