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 1111 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? 278    303    186    292    276    205    208    236    278    198    208

a.Find the mean.The mean is ? ​pound(s).​(Type an integer or a decimal rounded to one decimal place as​needed.)b. Find the median.The median is ? ​pound(s).​(Type an integer or a decimal rounded to one decimal place as​needed.)c. Find the mode.

Answer 1

Answer:  a. 242.5 pounds

b.  236 pounds

c . 208 and 278 pounds

The results are unlikely to be representative of all players in that​ sport's league because players randomly selected from championship sports team not the whole league.

Step-by-step explanation:

Given : Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team.

278    303    186    292    276    205    208    236    278    198    208

Mean = $\dfrac{\text{Sum of weights of all players}}{\text{Number of players}}$

$=\dfrac{278+303+186+292+276+205+208+236+278+198+208}{11}\\\\=\dfrac{2668}{11}\approx242.5\text{ pounds}$

For median , first arrange weights in order

186, 198 , 205 , 208, 208 , 236 , 276 , 278 ,278, 292 , 303

Since , number of data values is 11 (odd)

So Median = Middlemost value = 236 pounds

Mode = Most repeated value= 208 and 278

The results are unlikely to be representative of all players in that​ sport's league because players randomly selected from championship sports team not the whole league.

Answer 2

The mean, median and mode values of the distribution are :

• 242.5, 236 and (208 and 278) respectively.

Given the data :

• 278, 303, 186, 292, 276, 205, 208, 236, 278, 198, 208

Arrange the data in ascending order :

• 186, 198, 205, 208, 208, 236, 276, 278, 278, 292, 303

The mean = ΣX/ n

• Where, n = sample size = 11

• Mean = (186 + 198 + 205 + 208 + 208 + 236 + 276 + 278 + 278 + 292 + 303) / 11

• Mean = 2668 / 11

• Mean = 242.545

The median ;

• Since the data has been arranged :
• 1/2(n + 1)th
• 1/2(11 + 1)th = 1/2(12)th = 6th value

• The 6th value in the ordered data is 236

• Hence, the median = 236

The mode :

• The mode of the distribution is the most frequently occurring value :
• The most frequently occurring values are : 208 and 278 with frequency values of 2.

Therefore ;

Mean = 242.5 pounds

Median = 236 pounds

Mode = 208 and 278

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