Question 6

A population consists of the following 6 values: {10, 20, 30, 40, 50, 60). A sample of size 3 will be chosen from this

population without replacement and the median of the sample will be computed:

In other words, in a sample of size n = 3 ordered from smallest to largest the median is the 2nd number.

1. The median of a discrete random variable, , is defined as the value of such that

P(X

and

P(X>) ≤ 0.5

Determine the median of the population. Think of the population as an equally likely sample space.

2. Determine the sampling distribution of the sample median, m for this population by (1) identifying all possible

samples (how many are there?), (2) calculating the median in each sample and (3) using that to determine the

probability of each median.

3. Calculate E (m)

4. Determine the standard error or the sample median