Problem Solving

What is the average (arithmetic mean) weight of the p people in a certain group if the average weight of the p/3 heaviest people is 201 lbs and the average weight of the rest of the people in the group is 150 lbs?

A) 167
B) 160
C) 175.5
D) 186
E) 217

Easy way, let p=3, then 1 person is 201 and other 2 are 150 each.
Hence average =( 201+ 2*150)/3 = 501/3 = 167

Let me know if this helps

eagleeye wrote:Easy way, let p=3, then 1 person is 201 and other 2 are 150 each.
Hence average =( 201+ 2*150)/3 = 501/3 = 167

Let me know if this helps

what if p=3 and 2 is 201 and 1 is 150??

diebeatsthegmat wrote: what if p=3 and 2 is 201 and 1 is 150??

Hi,

If 2 is 201 and 1 is 150, then you can calculate the Average in the same manner as eagleeye explained.

Average = (2*201 + 1*150)/3 = (2/3)*201 + (1/3)*150 = 184

This is called the concept of weighted mean.

(i) When the weight of 150 was higher, the Average (167) was closer to 150.
(ii) When the weight of 201 was higher, the Average (184) was closer to 201.
(iii) If the weight of 150 and 201 are equal, the average will be exactly in between them (175.5).