#!/usr/bin/env python3

from math import sqrt
# from itertools import islice

def variance(xs):
    n = len(xs)
    mu = sum(xs) / n
    # mu = 265.8
    # print(sum(map(lambda x: (x - mu)**2, xs)))
    s = sum(map(lambda x: (x - mu)**2, xs))
    var = s / n
    deriv = sqrt(var)
    # var = sqrt( / len(xs))

    print('\\begin{align*}')
    print(f'  n &= {n} \\\\')
    print(f'  \\mu &= \\frac{{{sum(xs)}}}{{n}} = {mu:.1f} \\\\')
    print(f'  s &= \\sum\\limits_{{i=1}}^{{n}} {{(x_i - \\mu)}}^2 \\\\')
    # print [mylist[i:i+4] ]
    first = True
    for i in range(0, n, 3):
        symbol = '=' if first else '+'
        l = xs[i:i+3]
        a = ' + '.join(map(lambda x: f'{{({x} - {mu:.1f})}}^2', l))
        first = False
        print(f'    &{symbol} {a} \\\\')

    print(f'    &= {s:.1f} \\\\')

    # a = ' + '.join(map(lambda x: f'({x} - {mu})^2', xs))
    print(f'  \\sigma^2 &= \\frac{{s}}{{n}} = {var:.1f} \\\\')
    print(f'  \\sigma &= \\sqrt{{\\sigma^2}} = {deriv:.1f}')
    print('\\end{align*}')

    print()
    print()
    print()
    print()

  # \mu &= 1595 / 4 = 398.75 \\
  # \sigma &= \sqrt{\frac{(403 - 398.75)^2 + (369 - 398.75)^2 + (405 - 398.75)^2 + (418 - 398.75)^2}{4}} = 10.5

def main():
    # for xs in [[808, 787], [403, 369, 405, 418], [258, 273, 257, 264, 293, 250], [140, 175, 186, 166, 159, 152, 172, 148, 151, 146]]:
    # for xs in [[258, 273, 257, 264, 293, 250]]:
    for xs in [[499322, 500678], [249504, 250451, 249818, 250227], [166430, 166861, 166269, 166937, 166623, 166880], [100424, 99650, 99307, 100305, 99403, 100562, 100277, 99875, 99911, 100286]]:
        variance(xs)

if __name__ == '__main__':
    main()