Measures of the Spread of the Data · Exercise 21

Following are the published weights (in pounds) of all of the 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) The middle 50% of the weights are from _______ to _______.
(f) If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
(g) Assume the population was the San Francisco 49ers. Find:
(a) the population mean, μ.
(b) the population standard deviation, σ.
(c) the weight that is two standard deviations below the mean.
(d) When Steve Young, quarterback, played football, he weighed 205 pounds. How many standard deviations above or below the mean was he?
(h) That same year, the mean weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit Smith weighed in at 209 pounds. With respect to his team, who was lighter, Smith or Young? How did you determine your answer?

OpenStax, Introductory Business Statistics 2e · §2.7 Measures of the Spread of the Data · Exercise 21