Measures of the Spread of the Data · Exercise 26

Following are the published weights (in pounds) of all of the football team members of the San Francisco 49ers from a previous year:
177, 205, 210, 210, 232, 205, 185, 185, 178, 210, 206, 212, 184, 174, 185, 242, 188, 212, 215, 247, 241, 223, 220, 260, 245, 259, 278, 270, 280, 295, 275, 285, 290, 272, 273, 280, 285, 286, 200, 215, 185, 230, 250, 241, 190, 260, 250, 302, 265, 290, 276, 228, 265

(a) Organize the data from smallest to largest value.
(b) Find the median.
(c) Find the first quartile.
(d) Find the third quartile.
(e) Construct a box plot of the data.
(f) The middle 50 percent of the weights are from ________ to ________.
(g) If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
(h) If our population included every team member who ever played for a California-based football team, would the above data be a sample of weights or the population of weights? Why?
(i) Assume the population was a California-based football team. Find
(a) the population mean, μ,
(b) the population standard deviation, σ, and
(c) the weight that is two standard deviations below the mean.
(d) In addition, when the team's most famous quarterback, played football, he weighed 205 pounds. Also find how many standard deviations above or below the mean was he?
(j) That same year, the mean weight for a player from a Texas football team was 240.08 pounds with a standard deviation of 44.38 pounds. One player weighed in at 209 pounds. With respect to his team, who was lighter, the California quarterback or the Texas player? How did you determine your answer?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §2.7 Measures of the Spread of the Data · Exercise 26