In Exercises 7–10, use the same population of {4, 5, 9} that w...

Question

In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Median

c. Find the mean of the sampling distribution of the sample median.

Accepted Answer

Welcome back, everyone. Consider the population 2614. Calculate the mean of the sampling distribution of the median if samples of size N equals 2 are randomly selected with replacement. A says 6.2, B 7.3, C 9.8. And the 11.3. So first of all, we're given our population consisting of 26, and 14, and we want to form samples of size and equals 2 with replacement. So those will be 2.2, we can take the first element and we can repeat it, right? Followed by 26. And then 214. Now, if we take sex. We can make 6.2. Then we can take 6.6 and 6.14. Finally, if we take 14, we can form 14.2. 14.6. And 1414. Now what we're going to do is simply identify the median values of each sample. So we're going to say medium. And because we have two values in each sample, the median value is just the average value between the two values. So for 2.2, we get 2 + 2 divided by 2. Which is 2 Then we take 2.6, and we find the average as 2 + 6 divided by 2, which is 4. Followed by 2.14. We find the average of that 2 + 14 divided by 2, which is 8. Then we have 6.2. 6 + 2 divided by 2 gives us 4. Then we have 6.6. 6 + 6 divided by 2 is 6. Followed by 6.14. That would be 6 + 14 divided by 2, which is 10. And now we can move on to 14.2. The average value of that would be 14 + 2 divided by 2, which is 8. Then we have 14.6. We take 14 + 6 and divide it by 2. Which is 10. And finally, 1414. We take 14 + 14 divided by 2, and we get 14. Now with all of these median values, what we have to do is simply find The mean value. So let's label our median values. We have 24 8. 46, 10, 8, 10, and 14. We have a total of 123456789 medians. So to find the mean value, we basically have to add them up. 2 + 4 + 8 + 4+. 6 + 10 + 8 + 10 + 14, and we divide by the total sample size of 9, right? We get 22 divided by 3, which is equal to 7.3. And this corresponds to the answer choice B, so let's label our final answer, and thank you for watching.

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Key Concepts

Sampling Distribution

Sample Median

Mean of the Sampling Distribution

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