Averages

How do we calculate averages?

 average or mean   Definition: The result of adding all numbers in a set then dividing by amount of numbers. Examples : 1) The average of 1 and 5 is 3 because (1+5)/2= 3 2) The average of 1, 5, and 9 is 5 because(1+5+9)/3=5 Related Links Interactive activity involving median and mean

SAT PROBLEM
( 2nd problem in a 25 problem section )

2. The average (arithmetic mean) of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?

• 50
• 55
• 60
• 65
• 70
(Sunday/5.1997 #2) p. 483
 E. 70    3*60=180, which is the total number of points earned; the two numbers we do know are 50 and 60 which add up to 110     The third number is 180-110=70 since all three numbers must add up to 180 TEST METHOD: AVERAGE PIE    Use the average pie to chart out what you know and simplify this problem.

SAT PROBLEM
( 8th problem in 25 problem section)

In the triangles below what is the average (arithmetic mean) of a , b, c, x, and y?

• 21
• 45
• 50
• 52
• 54
(Sunday/5.1997 #8) p. 450 *
 E. 54    x+y=90 since the other angle is 90o and a triangle has 180o in total;     a, b and c must total 180o TEST METHOD: AVERAGE PIE  Tip:  Total --> degrees=180+180=360, the total number of degrees in two triangles.

SAT PROBLEM
#5 in a 10 problem section

In a certain game, each of the 5 players received a score between 0 and 100 inclusive. If their average(arithmetic mean) score was 80, what is the greatest possible number of the 5 players who dould have received a score of 50?

• None
• One
• Two
• Three
• Four
( Saturday/5.2002 #5) p.675 *
 C) METHOD: AVERAGE PIE. You know the total (5*80=400); you know the number (5), and you know the average(80). You also know the answer is between 0-4. By Trial and error you should be able to answer this one. KEYWORDS: "greatest possible" , "inclusive" If you're clueless, NO MATTER what you should be able to elimante A and guess. If you couldn't eliminate A, review how to solve average problems.

MEDIUM-HARD SAT PROBLEM:
(17th problem in 25 problem section )

17. The average (arithmetic mean) of a, b, and c is equal to the median of a, b, and c. If 0 < a < b < c, which of the following must be equal to b ?

• (a+c)/2
• (a+c)/3
• (c-a)/2
• (c-a)/3
(Saturday/1.2002 #17 ) p. 610
 A. (a+c)/2     TEST KEYWORD: "MUST" Plug in numbers for a,b,c and see which answer 'must' work.

 MEDIUM SAT PROBLEM: The average(arithmetic mean) of nine numbers is 9. When a tenth number is added the average of the ten numbers is also 9. What is the tenth number ? 0 9/10 10/9 9 10 A. Eliminate some obvious wrong ones B. , C., E. Remember to always estimate and have a good rough estimate of where the answers should be which is right around the original average of 9; if you added a new number that was much higher or lower like say 0 or 1,000 the average could never remain 9. TEST TRAP: D is atrap and since you're not dealing with the first few problems you should not have gone on without really thinking about his one

 VERY HARD SAT PROBLEM ( This is the 25th problem in 25 problem section ) If the average (arithmetic mean) of x, 2x-8, 2x+2, 3x-1, and 4x+1 is 6, what is the value of the mode of these numbers? (Student Generated Response) (Saturday/1.2000 SAT) #25 p. 540 8 If you're not shooting for at least a 700, you should skip the most difficult ones in the seciton; however, for those truly bold standardized test takers, a helpful hint with this one is to always remember to substitute in real number for algebraic variables like x (avoid ugly numbers like 19), then proceed through the problem. METHOD: PLUG IN ACTUAL NUMBERS TRAP: This problem is a series of traps! Good luck!

HARD SAT PROBLEM
( 25 th problem in a 25 problem section )

The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average is 86. What is the value of (p/n)?