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? 278 279 185 299 245 281 291 234 278 227 281

Answer 1

Answer:

• Mean = 261.63 pounds
• Median = 278 pounds
• Modes: 278 & 281
• Mid-range = 242
• Yes all the results will be able to represent all players in the sports league

Step-by-step explanation:

First of all, we will sort the data.

185 227 234 245 278 278 279 281 281 291 299

Mean:

Mean is defined as the sum of values divided by the number of values.

n = 11

$Mean = \frac{sum}{n}\\= \frac{185+227 +234+ 245+ 278+ 278+ 279+ 281+ 281+ 291+ 299}{11}\\=\frac{2878}{11}\\=261.63\ pounds$

Median:

As the number of values is odd,

The median will be:

$Median = (\frac{n+1}{2})th\ value\\= \frac{11+1}{2}\\=\frac{12}{2}\\=6th\ value$

The 6th value is 278

Median = 278

Mode:

Mode is the most frequent value in a data set.

In the given dataset,

278 and 281 are modes as both are repeated twice

Mid-range:

Mid-range is the average of maximum and minimum value

So,

Min = 185

Max = 299

So,

$Mid-range = \frac{Max+Min}{2}\\= \frac{185+299}{2}\\= \frac{484}{2}\\= 242$

Hence,

• Mean = 261.63 pounds
• Median = 278 pounds
• Modes: 278 & 281
• Mid-range = 242
• Yes all the results will be able to represent all players in the sports league