A population is formed my placing 5 balls labelled 1,2,3,4 and 5 respectively. Mean of this population is 3. Someone who does not know the contents of this bag will estimate the balue of mean by randomly taking a sample of 3 of the balls( without replacement) and finding either the sample mean or the sample median.
In the meantime, a statistician has listed all the possible samples of size 3 (sampling w/o replacement) and has calculated the sample mean and sample median for each possible sample. He finds that
All possible sample means form a distribution whose mean is 3 and whose SD is 0.577
All possible sample medians form a distribution whose mean is 3 and whose SD is 0.775
Regarding the choice between using sample mean and sample median for estimating population mean, which of the following is true?
A) Both sample mean and sample median are unbiased, but sample median is preferable as it has larger SD
B) Both sample mean and sample median are unbiased, but sample mean is preferable as it has smaller SD
C) Sample mean is unbiased and sample median is biased, so sample mean is preferable
D) Sample median is unbiased and sample mean is biased, so sample median is preferable
E) Both sample mean and median are biased
