Median

How do we find the Median of a set of numbers?

Median 

Definition: The number in the middle of a set ordered from least to greatest.

    Examples :
  • 2 is the median in the set {1,2,3}
  • 2 is also the median in the set {1,1,1,2,4,4,4}
  • 33 is also the median in the set {-1,0,1,33,40, 410, 411}

If you there is no number exactly in the middle of a set, then the median is the mean of the two middlemost numbers.

    Examples :
  • The median in the set {1, 2} is (1+2)/2 = 1.5
  • The median in the set {1, 1, 1, 2, 4, 4} is (1+2)/2 = 1.5
  • In the set {-12,-4, 0 , 20, 22, 234} the median is (0+2 )/2 =1


Related Links

Definition and problems involving the mean

Interactive activity involving median and mean


SAT PROBLEM
SAT Problem

The sum of four consecutive odd integers w,x,y and z is 24. What is the median of the set{w, x, y, z, 24}?

  • 3
  • 5
  • 7
  • 9
  • 24
( Saturday/5.2002 #14) p.658 *
 

SAT PROBLEM
#24 in a 25 problem section

In a set of eleven different numbers, which of the following CANNOT affect the value of the median?

  • Doubling each number
  • Increasing each number by 10
  • Increasing the smallest number only
  • Decreasing the largest number only
  • Increasing the largest number only
( Saturday/5.1997 #24) p.454 *
 

SAT PROBLEM
Mr. Morris Generated Question

In a set of eleven different numbers, which of the following CANNOT affect the value of the median?

  • Doubling each number
  • Decreasing the smallest number
  • Increasing the smallest number only
  • Decreasing the largest number only
  • Increasing each number by 10
(twist on the following actual SAT question: Saturday/5.1997 #24) p.454 *