The 11th Edition Of The Pro Football Encyclopedia Provided The Following Information: A Random Sample Of Pro Football Player Ages In Years Is Given As:$\[ \begin{array}{l} 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 22,

**The 11th Edition of The Pro Football Encyclopedia: A Statistical Analysis of Pro Football Player Ages**

The 11th Edition of The Pro Football Encyclopedia provides a wealth of information on professional football players, including their ages. In this article, we will analyze a random sample of pro football player ages in years to gain insights into the distribution of player ages.

The data provided by The 11th Edition of The Pro Football Encyclopedia is as follows:

$${ \begin{array}{l} 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 22, \end{array} }$$

Q: What is the mean age of the pro football players in the sample?

A: To calculate the mean age, we need to sum up all the ages and divide by the total number of players. The sum of the ages is 18 + 18 + 19 + 19 + 19 + 19 + 20 + 20 + 20 + 20 + 21 + 21 + 21 + 22 + 22 + 22 + 22 + 22 + 22 = 384. There are 19 players in the sample. Therefore, the mean age is 384 / 19 = 20.21 years.

Q: What is the median age of the pro football players in the sample?

A: To calculate the median age, we need to arrange the ages in order from smallest to largest. The ages in order are 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 22. Since there are 19 players (an odd number), the median is the middle value, which is the 10th value. The 10th value is 20.

Q: What is the mode of the pro football players in the sample?

A: The mode is the age that appears most frequently in the sample. From the data, we can see that the age 19 appears 5 times, which is more than any other age. Therefore, the mode is 19.

Q: What is the range of the pro football players in the sample?

A: The range is the difference between the largest and smallest ages in the sample. The largest age is 22 and the smallest age is 18. Therefore, the range is 22 - 18 = 4 years.

Q: What is the interquartile range (IQR) of the pro football players in the sample?

A: To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data. The lower half of the data is 18, 18, 19, 19, 19, 19, 20, 20, 20, 20. The median of this half is 19.5. The upper half of the data is 21, 21, 21, 22, 22, 22, 22, 22, 22. The median of this half is 22. Therefore, the IQR is Q3 - Q1 = 22 - 19.5 = 2.5.

Q: What is the standard deviation of the pro football players in the sample?

A: To calculate the standard deviation, we need to find the variance first. The variance is the average of the squared differences from the mean. The squared differences from the mean are (18-20.21)^2, (18-20.21)^2, (19-20.21)^2, (19-20.21)^2, (19-20.21)^2, (19-20.21)^2, (20-20.21)^2, (20-20.21)^2, (20-20.21)^2, (20-20.21)^2, (21-20.21)^2, (21-20.21)^2, (21-20.21)^2, (22-20.21)^2, (22-20.21)^2, (22-20.21)^2, (22-20.21)^2, (22-20.21)^2, (22-20.21)^2. The sum of these squared differences is 1.21 + 1.21 + 1.21 + 1.21 + 1.21 + 1.21 + 0.0004 + 0.0004 + 0.0004 + 0.0004 + 0.84 + 0.84 + 0.84 + 3.21 + 3.21 + 3.21 + 3.21 + 3.21 + 3.21 = 24.21. The variance is 24.21 / 19 = 1.27. The standard deviation is the square root of the variance, which is √1.27 = 1.13.

Q: What is the coefficient of variation (CV) of the pro football players in the sample?

A: The CV is the ratio of the standard deviation to the mean. The standard deviation is 1.13 and the mean is 20.21. Therefore, the CV is 1.13 / 20.21 = 0.056.

Q: What is the 95% confidence interval for the mean age of the pro football players in the sample?

A: To calculate the 95% confidence interval, we need to use the formula: (x̄ - (t * s / √n), x̄ + (t * s / √n)), where x̄ is the sample mean, t is the t-statistic, s is the sample standard deviation, and n is the sample size. The sample mean is 20.21, the sample standard deviation is 1.13, and the sample size is 19. The t-statistic for a 95% confidence interval with 18 degrees of freedom is 2.101. Therefore, the 95% confidence interval is (20.21 - (2.101 * 1.13 / √19), 20.21 + (2.101 * 1.13 / √19)) = (20.21 - 0.63, 20.21 + 0.63) = (19.58, 20.84).

Q: What is the 95% confidence interval for the median age of the pro football players in the sample?

A: To calculate the 95% confidence interval for the median, we need to use the formula: (m - (t * s / √n), m + (t * s / √n)), where m is the sample median, t is the t-statistic, s is the sample standard deviation, and n is the sample size. The sample median is 20, the sample standard deviation is 1.13, and the sample size is 19. The t-statistic for a 95% confidence interval with 18 degrees of freedom is 2.101. Therefore, the 95% confidence interval is (20 - (2.101 * 1.13 / √19), 20 + (2.101 * 1.13 / √19)) = (20 - 0.63, 20 + 0.63) = (19.37, 20.63).

Q: What is the 95% confidence interval for the mode of the pro football players in the sample?

A: To calculate the 95% confidence interval for the mode, we need to use the formula: (m - (t * s / √n), m + (t * s / √n)), where m is the sample mode, t is the t-statistic, s is the sample standard deviation, and n is the sample size. The sample mode is 19, the sample standard deviation is 1.13, and the sample size is 19. The t-statistic for a 95% confidence interval with 18 degrees of freedom is 2.101. Therefore, the 95% confidence interval is (19 - (2.101 * 1.13 / √19), 19 + (2.101 * 1.13 / √19)) = (19 - 0.63, 19 + 0.63) = (18.37, 19.63).

Q: What is the 95% confidence interval for the range of the pro football players in the sample?

A: To calculate the 95% confidence interval for the range, we need to use the formula: (R - (t * s / √n), R + (t * s / √n)), where R is the sample range, t is the t-statistic, s is the sample standard deviation, and n is the sample size. The sample range is 4, the sample standard deviation is 1.13, and the sample size is 19. The t-statistic for a 95% confidence interval with 18 degrees of freedom is 2.101. Therefore, the 95% confidence interval is (4 - (2.101 * 1.13 / √19), 4 + (2.101 * 1.13 / √19)) = (