A logistics officer is analyzing the fuel consumption of five transport trucks. The data for the first four trucks is , , , and gallons. The fuel data for the fifth truck was lost, but the officer remembers that it consumed more fuel than any of the other four trucks. If the mean fuel consumption of all five trucks is exactly equal to their median, how many gallons of fuel did the fifth truck consume?
- A
- B
- Cevap
- D
Cevap
The fifth truck consumed gallons of fuel.
Since the fifth truck consumed more fuel than the other four, the sorted order of the five values is , , , , and . The median of these five values is the third value, which is . The problem states that the mean equals the median, so the equation is . Simplifying the numerator gives . Multiplying both sides by results in . Subtracting from both sides gives .
Adım Adım Çözüm
Anahtar Kavram
Solving for an unknown data point by equating the mean and the median of an ordered dataset.