re of X = 84. Would you prel = = 10? (Hint: he location of

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can someone help me with this please ?

Certainly! Below is the transcription of the provided image, formatted for an educational website.

---

### Chapter 4: Measures for Variability

7. **On an exam with a mean of \( M = 78 \), you obtain a score of \( X = 84 \).**
   a. Would you prefer a standard deviation of \( s = 2 \) or \( s = 10 \)? (Hint: Sketch each distribution and find the location of your score.)
   
   b. If your score were \( X = 72 \), would you prefer \( s = 2 \) or \( s = 10 \)? Explain your answer.

8. **Calculate the mean and SS (sum of squared deviations) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use.**
   
   Sample A: \( 1 \quad 4 \quad 8 \quad 5 \)
   
   Sample B: \( 3 \quad 0 \quad 9 \quad 4 \)

9. **For the following population of \( N = 6 \) scores:**

   \( 3 \quad 1 \quad 4 \quad 3 \quad 3 \quad 4 \)
   
   a. Sketch a histogram showing the population distribution.
   
   b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2).
   
   c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of \(\sigma\)?)

10. **For the following sample of \( n = 7 \) scores:**

    \( 8 \quad 6 \quad 5 \quad 6 \quad 3 \quad 5 \quad 1 \)
    
    a. Sketch a histogram showing the sample distribution.
    
    b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.5).
    
    c. Compute SS, variance, and standard deviation for the sample. (How well does your estimate compare with the actual value of \( s \)?)

11. **For the following population of \( N = 6 \) scores:**

    \( 11 \quad 0 \quad
Transcribed Image Text:Certainly! Below is the transcription of the provided image, formatted for an educational website. --- ### Chapter 4: Measures for Variability 7. **On an exam with a mean of \( M = 78 \), you obtain a score of \( X = 84 \).** a. Would you prefer a standard deviation of \( s = 2 \) or \( s = 10 \)? (Hint: Sketch each distribution and find the location of your score.) b. If your score were \( X = 72 \), would you prefer \( s = 2 \) or \( s = 10 \)? Explain your answer. 8. **Calculate the mean and SS (sum of squared deviations) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use.** Sample A: \( 1 \quad 4 \quad 8 \quad 5 \) Sample B: \( 3 \quad 0 \quad 9 \quad 4 \) 9. **For the following population of \( N = 6 \) scores:** \( 3 \quad 1 \quad 4 \quad 3 \quad 3 \quad 4 \) a. Sketch a histogram showing the population distribution. b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2). c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of \(\sigma\)?) 10. **For the following sample of \( n = 7 \) scores:** \( 8 \quad 6 \quad 5 \quad 6 \quad 3 \quad 5 \quad 1 \) a. Sketch a histogram showing the sample distribution. b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.5). c. Compute SS, variance, and standard deviation for the sample. (How well does your estimate compare with the actual value of \( s \)?) 11. **For the following population of \( N = 6 \) scores:** \( 11 \quad 0 \quad
```markdown
**PROBLEMS**

1. Why is it necessary to have more than one method for measuring central tendency?

2. Find the mean, median, and mode for the following sample of scores:
   - 5, 4, 5, 2, 7, 1, 3, 5

3. Find the mean, median, and mode for the following sample of scores:
   - 3, 6, 7, 3, 9, 8, 3, 7, 5

4. Find the mean, median, and mode for the scores in the following frequency distribution table:

   | x | f |
   |---|---|
   | 6 | 1 |
   | 5 | 2 |
   | 4 | 2 |
   | 3 | 2 |
   | 2 | 2 |
   | 1 | 5 |

5. Find the mean, median, and mode for the scores in the following frequency distribution table:

   | x | f |
   |---|---|
   | 8 | 1 |
   | 7 | 1 |
   | 6 | 2 |
   | 5 | 5 |
   | 4 | 2 |
   | 3 | 2 |

6. For the following sample:

   a. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution.

   b. Assume that the scores are measurements of a discrete variable and find the median.

   - Scores: 1, 2, 3, 3, 4

7. A population of N = 15 scores has ΣX = 120. What is the population mean?

8. A sample of n = 8 scores has a mean of M = 12. What is the value of ΣX for this sample?

9. A population with a mean of μ = 8 has ΣX = 40. How many scores are in the population?

10. A sample of n = 7 scores has a mean of M = 9. If one new person with a score of X = 11 is added to the sample, what is the value for the new mean?

11. A sample of n = 6 scores has a mean of M = 13. If one person with a score of X = 3
Transcribed Image Text:```markdown **PROBLEMS** 1. Why is it necessary to have more than one method for measuring central tendency? 2. Find the mean, median, and mode for the following sample of scores: - 5, 4, 5, 2, 7, 1, 3, 5 3. Find the mean, median, and mode for the following sample of scores: - 3, 6, 7, 3, 9, 8, 3, 7, 5 4. Find the mean, median, and mode for the scores in the following frequency distribution table: | x | f | |---|---| | 6 | 1 | | 5 | 2 | | 4 | 2 | | 3 | 2 | | 2 | 2 | | 1 | 5 | 5. Find the mean, median, and mode for the scores in the following frequency distribution table: | x | f | |---|---| | 8 | 1 | | 7 | 1 | | 6 | 2 | | 5 | 5 | | 4 | 2 | | 3 | 2 | 6. For the following sample: a. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. b. Assume that the scores are measurements of a discrete variable and find the median. - Scores: 1, 2, 3, 3, 4 7. A population of N = 15 scores has ΣX = 120. What is the population mean? 8. A sample of n = 8 scores has a mean of M = 12. What is the value of ΣX for this sample? 9. A population with a mean of μ = 8 has ΣX = 40. How many scores are in the population? 10. A sample of n = 7 scores has a mean of M = 9. If one new person with a score of X = 11 is added to the sample, what is the value for the new mean? 11. A sample of n = 6 scores has a mean of M = 13. If one person with a score of X = 3
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