Why does Bessel's correction is biased downward as stated in wiki:
while the sample variance (using Bessel's correction) is an unbiased estimator of the population variance, its square root, the sample standard deviation, is a biased estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen's inequality.
But by Jensen inequality for a concave function, we have
f is the square root function, i.e. the sample standard deviation is greater than the expectation of the srandard deviation, i.e. its biased upward. Where am I wrong?