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

Definition and problems involving the median | average pie method

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
 

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?

Average of Two Triangles

  • 21
  • 45
  • 50
  • 52
  • 54
(Sunday/5.1997 #8) p. 450 *
 

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 *
 

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
 

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


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


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)?

(Student generated answer)

(Saturday/5.1997 SAT #25) p. 465 *


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

If the average(arithmetic mean) of three different positive integers is 70, what is the greatest possible value of one of the integers?
(Student generated answer)

(Saturday/11.1996 SAT #25) p. 385 *