Consider samples of size 3 selected from the population {3,6,9,15}. a. Calculate the sample mean, median and the range for each sample.

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c. Use 3 histograms to graph the sampling distributions in part b.

Just answer "c" but you might need to see the attached file.

**Sampling Distributions: Sample Mean, Median, and Range**

b. Find the sampling distributions of sample mean, median, and range by constructing 3 tables that show possible values and the associated probabilities.

### Table 1: Sample Mean (\(\bar{x}\))

| \(\bar{x}\) |        |
|-------------|--------|
| \(p(\bar{x})\) |        |

### Table 2: Sample Median (\(M\))

| \(M\)   |        |
|---------|--------|
| \(p(M)\) |        |

### Table 3: Sample Range (\(R\))

| \(R\)   |        |
|---------|--------|
| \(p(R)\) |        |
Transcribed Image Text:**Sampling Distributions: Sample Mean, Median, and Range** b. Find the sampling distributions of sample mean, median, and range by constructing 3 tables that show possible values and the associated probabilities. ### Table 1: Sample Mean (\(\bar{x}\)) | \(\bar{x}\) | | |-------------|--------| | \(p(\bar{x})\) | | ### Table 2: Sample Median (\(M\)) | \(M\) | | |---------|--------| | \(p(M)\) | | ### Table 3: Sample Range (\(R\)) | \(R\) | | |---------|--------| | \(p(R)\) | |
1. Consider samples of size 3 selected from the population {3, 6, 9, 15}.
   a. Calculate the sample mean, median, and the range for each sample.

**Table Explanation:**

- The table presents samples of size 3 drawn from the population {3, 6, 9, 15}.
- Each row represents a different sample combination.
- The columns are divided into four parts, each containing a "Sample" column and three statistic columns: \(\bar{x}\) (mean), \(M\) (median), and \(R\) (range).
  
**Sample Combinations:**

1. Sample: {3, 3, 3}
2. Sample: {3, 3, 6}
3. Sample: {3, 3, 9}
4. Sample: {3, 3, 15}
5. Sample: {3, 6, 3}
6. Sample: {3, 6, 6}
7. Sample: {3, 6, 9}
8. Sample: {3, 6, 15}
9. Sample: {3, 9, 3}
10. Sample: {3, 9, 6}
11. Sample: {3, 9, 9}
12. Sample: {3, 9, 15}
13. Sample: {3, 15, 3}
14. Sample: {3, 15, 6}
15. Sample: {3, 15, 9}
16. Sample: {3, 15, 15}

And similarly for combinations starting with 6, 9, and 15.

**Details:**
- Each statistic (\(\bar{x}\), \(M\), \(R\)) for every sample needs to be calculated:
  - \(\bar{x}\) is the average of the sample values.
  - \(M\) is the middle value when the sample is ordered.
  - \(R\) is the difference between the maximum and minimum values. 

Note: The table does not provide filled values for the mean, median, and range yet.
Transcribed Image Text:1. Consider samples of size 3 selected from the population {3, 6, 9, 15}. a. Calculate the sample mean, median, and the range for each sample. **Table Explanation:** - The table presents samples of size 3 drawn from the population {3, 6, 9, 15}. - Each row represents a different sample combination. - The columns are divided into four parts, each containing a "Sample" column and three statistic columns: \(\bar{x}\) (mean), \(M\) (median), and \(R\) (range). **Sample Combinations:** 1. Sample: {3, 3, 3} 2. Sample: {3, 3, 6} 3. Sample: {3, 3, 9} 4. Sample: {3, 3, 15} 5. Sample: {3, 6, 3} 6. Sample: {3, 6, 6} 7. Sample: {3, 6, 9} 8. Sample: {3, 6, 15} 9. Sample: {3, 9, 3} 10. Sample: {3, 9, 6} 11. Sample: {3, 9, 9} 12. Sample: {3, 9, 15} 13. Sample: {3, 15, 3} 14. Sample: {3, 15, 6} 15. Sample: {3, 15, 9} 16. Sample: {3, 15, 15} And similarly for combinations starting with 6, 9, and 15. **Details:** - Each statistic (\(\bar{x}\), \(M\), \(R\)) for every sample needs to be calculated: - \(\bar{x}\) is the average of the sample values. - \(M\) is the middle value when the sample is ordered. - \(R\) is the difference between the maximum and minimum values. Note: The table does not provide filled values for the mean, median, and range yet.
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