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

• 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

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 = (sum)/(n)\\= (185+227 +234+ 245+ 278+ 278+ 279+ 281+ 281+ 291+ 299)/(11)\\=(2878)/(11)\\=261.63\ pounds`

Median:

As the number of values is odd,

The median will be:

`Median = ((n+1)/(2))th\ value\\= (11+1)/(2)\\=(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 = (Max+Min)/(2)\\= (185+299)/(2)\\= (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