Question

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the data and then​ (e) answer the given question. Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that​ sport's league? 246    273    298    259    266    200    260    306    246    248    200 a. Find the mean. The mean is nothing ​pound(s). ​(Type an integer or a decimal rounded to one decimal place as​ needed.) b. Find the median. The median is nothing ​pound(s). ​(Type an integer or a decimal rounded to one decimal place as​ needed.) c. Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The​ mode(s) is(are) nothing ​pound(s). ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.) B. There is no mode. d. Find the midrange. The midrange is nothing ​pound(s). ​(Type an integer or a decimal rounded to one decimal place as​ needed.) e. Are the results likely to be representative of all players in that​ sport's league? A. The results are not likely to be representative because the championship team may not be representative of the entire league. B. The results are not likely to be representative because the median is not equal to the mode. C. The results are likely to be representative because a championship team is most likely representative of the entire league. D. The results are not likely to be representative because the median is not equal to the mean.

Answer 1

Solution:

a)

Mean = (246 + 273 + 298 + 259 + 266 + 200 + 260 + 306 + 246 + 248 + 200)/11
= 2802/11
Mean = 254.7273

b)

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

200   200   246   246   248   259   260   266   273   298   306   

So, the median is 259 .

c)

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

200   200   246   246   248   259   260   266   273   298   306   

Since both 200 and 246 occur 2 times, the modes are 200 and 246 ( this data set is bimodal).

d)

The minimum value of a data set (Min. Value): 200

The maximum value of a data set (Max. Value): 306

Midrange = (Min. Value + Max. Value) / 2 = (200 + 306) / 2 = 253