Three randomly selected households are surveyed. The numbers of people in the ho

Question

Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 12.

Assume that samples of size n = 2 are randomly selected with replacement form the population of 2, 4, and 12.

Listed below are the nine different samples.

2,2   2,4   2,12   4,2 4,4   4,12 12, 2 12,4   12,12

a). Find the median of each of the nine samples, then summarize the sampling distrinution fo the medians in the format of a table representing the probability distribution of the distinct median values.

Solve: Sample Median                      Solve: Probability

I do not know how to solve for the sample median. Could you please explain how to solve for each sample meidan. That's really the only thing that I do not understand.

Explanation / Answer

Since there are two data values is the sample so median will be average of these two data values. That is median will equal to median. Since each sample is equally likely so probability of each sample is 1/9. Folloiwng table shows the same:

Following is the probability distribution of median:

Samples Median P(median) 2 2 2 0.11111111 2 4 3 0.11111111 2 12 7 0.11111111 4 2 3 0.11111111 4 4 4 0.11111111 4 12 8 0.11111111 12 2 7 0.11111111 12 4 8 0.11111111 12 12 12 0.11111111

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