How many more observations the median needs

For a normal sample, the asymptotic relative efficiency of the sample median relative to the sample mean is 2/\pi. A mean of 64 observations has a certain asymptotic variance. How many observations does the median need to match that variance? Use \pi/2\approx 1.571.

The asymptotic variance of the median is (\pi/2) times the asymptotic variance of the mean, for the same n. Matching the variance means multiplying the median’s sample size by \pi/2\approx 1.571. For a mean of 64 observations the median needs 64\times 1.571\approx 100.5 observations, so 101 if the count has to be an integer.