The HIV virus has a high mutation rate compared with bacteria and multicellular life. Many of these mutations are bad for the virus, causing it to replicate more slowly. Theys et al. (2018) assembled a very large database of known HIV mutants and their replication rates.

We took a random sample of 100 mutants from this database using the computer and calculated the sample median replication rate and the sample mean rate. We repeated this process a vast number of times, calculating the sample median and mean each time. The standard deviation of the distribution of sample means was 0.00073. The standard deviation of the distribution of sample medians was 0.0224.

a. What is the standard error of the mean replication rate?

b. What is the standard error of the median replication rate?

c. Which measure of the central tendency (mean or median) is likely to be estimated with greater precision if a random sample of 100 data mutants is sampled from the database: the mean or the median?

Explain your answer.