Realistic

• Weighted averages are more realistic. A standard average assumes that everything is created equal, but in the real world this is not the case. So by assigning different weights to things with different values, you can come up with a more realistic average. A good way to understand this is to look at actual weights. Assume you want to find the average number of blocks in each of three boxes. However, the blocks are made of different materials and therefore weigh different amounts. If you multiply each box by its weight, you will streamline the whole process and compare the actual sizes of the blocks rather than an arbitrary number of blocks.
  
  So if the first box weighs 5 pounds and has 2 blocks in it, the second box weighs 10 pounds and has 1 block in it, and the third block has 5 blocks in it and weighs 5 pounds, you would find your average like this:
  
  (5 x 2) + (10 x 1) + (5 x 5) = 45
  
  45/3 = 15. The weighted average is 15.
  
  

Flexibility

• Weighted averages are flexible. You can multiply the numbers in your series by anything you want to show their weight. This is advantageous because it lets statisticians adjust numbers to fit their exact situation. Standard averages, on the other hand, cannot compensate for real-world differences between situations, and are therefore not as useful.
  
  Assume you are comparing two basketball players. The first made 10 shots in one game, 20 shots in another and 15 shots in a third. His average shots per game is 15. The second basketball player made 5 shots in his first game, 10 in his second and 15 in his third. He made an average of 10 shots per game.
  
  However, assume the first basketball player is in his fourth season and the second basketball player is still in his first. This experience difference needs to be compensated for. So assume you're giving every shot the first basketball player makes a weight of 1 and the second player's shots a weight of 2 to compensate for the fact that he has not been playing for as long.
  
  This dramatically changes the results. The first basketball player's weighted average is still 45, because every number was multiplied by 1. The second's, however, is now thus:
  
  (5 x 2) + (10 x 2) + (15 x 2) = 60
  
  60/3=20
  
  The second player's weighted average is now 20, which more accurately reflects his skill level.
  
  

Stock Indexing

• Stock indexes often use a price weight to determine the value of the index as a whole. This is advantageous because it keeps lower-price stocks from having a disproportionate effect. By making the higher stocks affect the value of the average more than the lower stocks do, it is possible to create a more accurate picture of the value of the index as a whole.
  
  Other indexes are weighted by other things, such as market capitalization. This shows the subjective nature of company valuing, but either way, a weighted average lets the more-valued companies affect the price more.
  
  For a simple example, assume you have one stock worth $20 per share and another worth $50 per share. If you were going to index these stocks, the average price would be $35.
  
  However, assume it is weighted for market capitalization. The first company has a market capitalization of $100 while the second has a market capitalization of $20 (remember, this is simplified). Each of the first stocks is now worth five of the second stocks. So the average price is now $75 --- $60 of which comes from the first stock, even though it costs only $20 per share.
  
  

Clarity in Grading

• Weighted averages are often used in high schools and universities. The advantage for grading is that tests require more effort than quizzes, which in turn require more effort than attendance and class participation. So weighting the students' average grades makes each assignment's relative importance more clear.
  
  Assume a professor makes his final exam worth 70 percent of the final mark and an essay worth 30 percent. A student gets 80 percent on the final exam and 70 percent on the essay. Each of these values needs to be multiplied by what it is worth:
  
  80% = 80/100
  
  80 x 0.7 = 56
  
  30% = 30/100
  
  70 x 0.3 = 21
  
  56 + 21 = 77.
  
  The student receives 77 percent as his final grade due to the fact that the final exam was worth so much more than the essay.