"""Synthetic interval example; not real measurements. Python standard library only."""
from math import sqrt
from statistics import mean, stdev

x = [8, 9, 9, 10, 10, 10, 11, 11, 12, 10]
n, centre, s = len(x), mean(x), stdev(x)
t = 2.2621571627409915  # 0.975 quantile, 9 degrees of freedom
ci = t * s / sqrt(n)
pi = t * s * sqrt(1 + 1/n)
if __name__ == "__main__":
    print(tuple(round(v, 4) for v in (centre-ci, centre+ci)))
    print(tuple(round(v, 4) for v in (centre-pi, centre+pi)))