Question

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.

178; 203; 212; 212; 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

Organize the data from smallest to largest value.

Part (a)

Find the median.

Part (b)

Find the first quartile. (Round your answer to one decimal place.)

Part (c)

Find the third quartile. (Round your answer to one decimal place.)

Part (d)

The middle 50% of the weights are from to .

Part (e)

If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why? (choose one)

-The above data would be a sample of weights because they represent a subset of the population of all football players.

-The above data would be a sample of weights because they represent all of the players from one year.    

-The above data would be a population of weights because they represent all of the football players.

-The above data would be a population of weights because they represent all of the players on a team.

Part (f)

If our population were Football Team A, would the above data be a sample of weights or the population of weights? Why? (choose one)

-The data would be a sample of weights because they represent all of the professional football players.

-The data would be a population of weights because they represent all of the players on Football Team A.   

- The data would be a sample of weights because they represent all of the players on Football Team A.

-The data would be a population of weights because they represent all of the professional football players.

Part (g)

Assume the population was Football Team A. Find the following. (Round your answers to two decimal places.)

(i) the population mean, ? ______

(ii) the population standard deviation, ? _____

(iii) the weight that is 3 standard deviations below the mean ____

(iv) When Player A played football, he weighed 229 pounds. How many standard deviations above or below the mean was he? _____

standard deviations _______ (above or below) the mean

Part (h)

That same year, the average weight for Football Team B was 240.08 pounds with a standard deviation of 44.38 pounds. Player B weighed in at 209 pounds. Suppose Player A from Football Team A weighed 229 pounds. With respect to his team, who was lighter, Player B or Player A? How did you determine your answer? (choose one)

-Player A, because he is more standard deviations away from his team's mean weight.

-Player B, because he is more standard deviations away from his team's mean weight.    

-Player A, because Football Team A has a higher mean weight.

-Player B, because Football Team B has a higher mean weight.

Answer 1

a) First, we sort the data from smallest to largest values. Since we have 53 observations, therefore the (53+1)/2 = 27^th value in our ordered data set is the median.
     In our data set, therefore the median is 241.

b) The first quartile is given by n/4 where n is the number of observations in the data set.
     Therefore, in this case, the first quartile is the 53/4 = 13.25^th value in the ordered data set. Since 13.25 is not a whole number, the first quartile should lie between the 13^th and 14^th values in the ordered data set, which are 205 and 206 respectively. Therefore, the first quartile is 205+0.25*(206-205) = 205.3 (rounded to 1 decimal place).

c) The third quartile is given by 3n/4 where n is the number of observations in the data set.
     Therefore, in this case, the third quartile is the 3*53/4 = 39.75^th value in the ordered data set. Since 39.75 is not a whole number, the third quartile should lie between the 39^th and 40^th values in the ordered data set, which are 270 and 272 respectively. Therefore, the third quartile is 270+0.75*(272-270) = 271.5.

d) The middle 50% of weights will always lie between the first and the third quartile. Therefore, in this case, the middle 50% of weights lie between 205.3 and 271.5.

Please note, the problem has eight subparts. Only the first four subparts have been answered.