Worked solution P28-Easy-1. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-2. The mean is 22.29, the median is 22.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=22.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-3. The mean is 18.29, the median is 18.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=18.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-4. The mean is 23.29, the median is 23.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=23.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-5. The mean is 24.29, the median is 24.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=24.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-6. The mean is 25.29, the median is 25.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=25.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-7. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-8. The mean is 25.29, the median is 25.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=25.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-9. The mean is 29.29, the median is 29.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=29.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-10. The mean is 24.29, the median is 24.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=24.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-11. The mean is 22.29, the median is 22.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=22.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-12. The mean is 20.29, the median is 20.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=20.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-13. The mean is 23.29, the median is 23.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=23.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-14. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-15. The mean is 18.29, the median is 18.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=18.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-16. The mean is 15.29, the median is 15.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=15.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Easy-17. The mean is 21.29, the median is 21.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=21.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-1. The mean is 25.29, the median is 25.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=25.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-2. The mean is 24.29, the median is 24.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=24.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-3. The mean is 24.29, the median is 24.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=24.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-4. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-5. The mean is 21.29, the median is 21.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=21.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-6. The mean is 26.29, the median is 26.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=26.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-7. The mean is 15.29, the median is 15.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=15.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-8. The mean is 29.29, the median is 29.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=29.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-9. The mean is 16.29, the median is 16.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=16.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-10. The mean is 18.29, the median is 18.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=18.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-11. The mean is 25.29, the median is 25.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=25.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-12. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-13. The mean is 21.29, the median is 21.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=21.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-14. The mean is 15.29, the median is 15.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=15.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-15. The mean is 18.29, the median is 18.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=18.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-16. The mean is 24.29, the median is 24.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=24.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Tough-17. The mean is 20.29, the median is 20.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=20.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-1. The mean is 20.29, the median is 20.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=20.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-2. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-3. The mean is 15.29, the median is 15.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=15.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-4. The mean is 23.29, the median is 23.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=23.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-5. The mean is 23.29, the median is 23.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=23.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-6. The mean is 27.29, the median is 27.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=27.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-7. The mean is 18.29, the median is 18.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=18.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-8. The mean is 23.29, the median is 23.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=23.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-9. The mean is 18.29, the median is 18.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=18.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-10. The mean is 24.29, the median is 24.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=24.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-11. The mean is 29.29, the median is 29.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=29.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-12. The mean is 16.29, the median is 16.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=16.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-13. The mean is 19.29, the median is 19.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=19.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-14. The mean is 19.29, the median is 19.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=19.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-15. The mean is 23.29, the median is 23.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=23.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-16. The mean is 28.29, the median is 28.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=28.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.

Worked solution P28-Toughest-17. The mean is 26.29, the median is 26.00, and the sample standard deviation is 4.15. $$\overline{x}=\frac{\sum x_i}{7}=26.29,s=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}=4.15.$$ Interpretation: The mean is the balance point; s describes a typical distance from the mean in the variable's units. Validity: Use resistant summaries such as median and IQR when skewness or outliers make mean and standard deviation misleading. Error to reject: Do not divide the sample variance by n when the requested quantity is the conventional sample standard deviation s.