population median and mean

Statistics
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hree randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 3, 8, and 10. Consider the values of 3, 8, and 10 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 8, and 10. The nine different samples are as follows: (3, 3), (3, 8), (3, 10), (8, 3), (8, 8), (8, 10), (10, 3), (10, 8), and (10, 10).

(i) Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution. (ii) Compare the population median to the mean of the sample medians. (iii) Do the sample medians target the value of the population median? In general, do medians make good estimators of population medians? Why or why not?
Jul 3rd, 2015

Thank you for the opportunity to help you with your question!

the sample median is
1 3
2 3.5
3 7
4 3.5
5 4
6 7.5
7 7
8 7.5
9 11

  probability of the median
3 1/9
3.5 2/9
4 1/9
7 2/9
7.5 2/9
11 1/9

Mean of medians will be= (3,3.5,3.5,4,7,7,7.5,7.5,11) = 6
  median population  = 4

  medians are good estimators of population medians? no.
Median is a biased estimator unlike mean.

When it has only two numbers, just average the two numbers to find the median.
The median of 3,3 is 3
The median of 3,8 is (3+8)/2 = 5.5

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 3rd, 2015

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Jul 3rd, 2015
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Jul 3rd, 2015
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