MathRevolution wrote:
The range of the set is \(2\) times \(40 – x\), since \(40 – x\) is the distance between the median and the maximum. The minimum is the median minus the distance between the median and the maximum, which is \(x – ( 40 – x ) = 2x – 40\).
Therefore, the answer is B.
Answer : B
The only time the range = 2(maximum value - median) is when the median is the average of the minimum and maximum value.
For example, in the set {1, 9, 17}, the range = 17 - 1 = 16, which is equal to 2(maximum value - median)
However, the rule, range = 2(maximum value - median), does not work when the median is NOT the average of the minimum and maximum value.
For example, the set {-9, 39, 40} satisfies the given information
Here, x = 39, the maximum value is 40, and the range (of 49) is 10 greater than the median (39)
In this case, minimum value (-9) does NOT equal 2x - 40
Cheers,
Brent
You are right.
The question should be changed to the following.
It is fixed now.
The average of the maximum and the minimum of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than \(x\). What is the minimum of the set in terms of \(x\)?