SOLUTION: In a set of eleven different numbers, which of the following CANNOT affect the value of the median? A. Doubling each number B. Increasing each number by 10 C. Increasing the sma

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Question 341672: In a set of eleven different numbers, which of the following CANNOT affect the value of the median?
A. Doubling each number
B. Increasing each number by 10
C. Increasing the smallest number only
D. Decreasing the largest number only
E. Increasing the largest number only
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20086) (Show Source):
You can put this solution on YOUR website!
In a set of eleven different numbers, which of the following CANNOT affect the value of the median?

Let's say we had these 11 numbers in order smallest to largest: 2, 5, 7, 8, 12, 14, 18, 20, 24, 35, 57 then the median is the middle number, 14, which I have colored red.

A. Doubling each number

Let's double each number and see: 4, 10, 14, 16, 24, 28, 36, 40, 48, 70, 114 No, the median is affected, it changed from 14 to 28. So A is not a correct choice.

B. Increasing each number by 10

Let's increase each number by 10 12, 15, 17, 18, 22, 24, 28, 30, 34, 45, 67 No, the median is affected, it changed from 14 to 24. So B is not a correct choice.

C. Increasing the smallest number only

Let's increase the smallest number, 2, to 4 4, 5, 7, 8, 12, 14, 18, 20, 24, 35, 57 Yes, the median is not affected, for it is still 14. So C IS a correct choice.

D. Decreasing the largest number only

Let's decrease the largest number, 57, to 44 2, 5, 7, 8, 12, 14, 18, 20, 24, 35, 44 Yes, the median is not affected, for it is still 14. So D IS a correct choice.

E. Increasing the largest number only

Let's increase the largest number, 57, to 68 2, 5, 7, 8, 12, 14, 18, 20, 24, 35, 68 Yes, the median is not affected, for it is still 14. So E IS a correct choice. Edwin

Answer by MathTherapy(10858) (Show Source):
You can put this solution on YOUR website!
In a set of eleven different numbers, which of the following CANNOT affect the value of the median?
A. Doubling each number
B. Increasing each number by 10
C. Increasing the smallest number only
D. Decreasing the largest number only
E. Increasing the largest number only

CHOICE A. Doubling each number WILL DEFINITELY CHANGE the value of the median.

CHOICE B.
Increasing each number by 10 WILL DEFINITELY CHANGE the value of the median.

CHOICE C.
Increasing the smallest number only CAN POSSIBLY CHANGE the value of the median, especially if it is increased to a value greater than the median.

CHOICE D.
Decreasing the largest number only CAN POSSIBLY CHANGE the value of the median, especially if it is decreased to a value less than the median.

Increasing the largest number only MOST DEFINITELY WILL NOT CHANGE the value of the median, as the median maintains its value and will be in the same position as before - the position of the center or middle value in the set of data values.