Question

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; 2651)The middle 50% of the weights are from _____ to _______ ?2) If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why? a. The above data would be a sample of weights because they represent a subset of the population of all football players. b. The above data would be a sample of weights because they represent all of the players from one year. c. The above data would be a population of weights because they represent all of the players on a team. d. The above data would be a population of weights because they represent all of the football players.

Answer 1

Answer:

206 to 272

Step-by-step explanation:

First, arrange the weights in ascending order:

177 174 178 184 185 185 185 185 188 190 200 205 205 206 210 210 210 212 212 215 215 220 223 228 230 232 241 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302

Once arranged, we find the quartiles. The quartiles separate 25% of the lowest and 25% of the highest population from the data, eventually leaving behind the middle 50% population:

$Q_1 = \frac{n}{4} ^{th} \ value \rightarrow \frac{53}{4} = 13.25^{th} \value \rightarrow 205 \\\\Q_3= \frac{3n}{4} ^{th} \ value \rightarrow \frac{53 \times 3}{4} = 39.75^{th} \value \rightarrow 272$

The middle 50% of the values lie from 206 to 272.

The data would be considered a sample because it only incorporates a subset of all the professional players, i.e. only the San Francisco 49ers, without taking into account all the other teams of professional football players.