Question

Heavy football players: Following are the weights, in pounds, for offensive and defensive linemen on a professional football team at the beginning of a recent year. Offense: 325 292 316 308 325 263 302 311 265 329 267 324 Defense: 265 276 255 306 317 281 268 282 260 261 256 286 (a) Find the mean and median weight for the offensive linemen. Round the answers to at least one decimal place. (b) Find the mean and median weight for the defensive linemen. Round the answers to at least one decimal place. (c) Do offensive or defensive linemen tend to be heavier, or are they about the same

Answer 1

a) Mean = 302.25, Median = 309.5

b) Mean = 276.08, Median = 272

c) Offensive linemen tends to be heavier.

Explanation:

We are given the following in the question:

Offense: 325, 292, 316, 308, 325, 263, 302, 311, 265, 329, 267, 324

Defense: 265, 276, 255, 306, 317, 281, 268, 282, 260, 261, 256, 286

a) mean and median weight for the offensive linemen

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(3627)/(12) = 302.25`

`Median:\\\text{If n is odd, then}\\\\Median = \displaystyle(n+1)/(2)th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle((n)/(2)th~term + ((n)/(2)+1)th~term)/(2)`

Sorted Data: 263, 265, 267, 292, 302, 308, 311, 316, 324, 325, 325, 329

`\text{Median} = (6^(th)+7^(th))/(2)=(308+311)/(2) = 309.5`

b) mean and median weight for the defensive linemen

`Mean =\displaystyle(3313)/(12) = 276.08`

Sorted Data: 255, 256, 260, 261, 265, 268, 276, 281, 282, 286, 306, 317

`\text{Median} = (6^(th)+7^(th))/(2)=(268+276)/(2) = 272`

c) Comparison

On comparing the mean and median of offensive and defensive linemen, offensive tends to be heavier