# 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 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 *
 C) 7 TRAP: Answer E) 24  Hopefully, you were suspiciuos of medium dificulty level question having an answer that is in the actual question. METHOD: PLUG IN actual values.

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 *
 E) METHOD: PLUG IN actual values; create a set of numbers (can be a set of 3 numbers) and try each out. You will see that only E will have no effect on the median, and it makes sense if you reason it out. The median, which is the middle value, does not care how big the largest is or how small the smallest is.

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 *
 B) This is the converse scenario of the question immediately above which is an actual SAT question. METHOD: PLUG IN actual values; create a set of numbers (can be a set of 3 numbers) and try each out. You will see that only B will have no effect on the median, and it makes sense if you reason it out. The median, which is the middle value, does not care how big the largest is or how small the smallest is.