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Zorluk: ZorMeasures of Central Tendency

A maintenance chief is reviewing the repair times (in hours) for five generators: 88, 1212, 1515, 99, and 1616. A sixth generator's repair time is added to the records. If the median repair time for all six generators is exactly 11.511.5 hours, what is the repair time of the sixth generator?

  1. A
    88
  2. B
    99
  3. 1111Cevap
  4. D
    2323

Cevap

The repair time of the sixth generator is 1111 hours.
The correct answer is found by first sorting the existing times into ascending order: 8,9,12,15,168, 9, 12, 15, 16. Because there will be six total items, the median is calculated by averaging the 3rd and 4th values. The 3rd value is 1212, and the target median is given as 11.511.5. This sets up the equation (12+x)/2=11.5(12 + x) / 2 = 11.5. Multiplying both sides by 22 gives 12+x=2312 + x = 23. Subtracting 1212 from both sides reveals the 6th generator's time must be 1111 hours.

Adım Adım Çözüm

1
Sort the known repair times in ascending order.
8,9,12,15,168, 9, 12, 15, 16
The median depends on the ordered sequence of data, not the order in which it was recorded.
2
Determine how the median is calculated for a six-item data set.
The median will be the average of the 3rd and 4th values in the sorted list.
For an even number of data points, the median is exactly halfway between the two central numbers.
3
Set up an equation using the known middle value and the target median.
The current 3rd value is 1212. The 4th value will be the new time xx. Equation: 12+x2=11.5\frac{12 + x}{2} = 11.5
We know the final median must be 11.511.5, and 1212 is the existing middle value that must be paired with xx to achieve this average.
4
Solve the equation for xx.
12+x=2312 + x = 23, which simplifies to x=11x = 11.
Multiplying both sides by 22 and then subtracting 1212 isolates the unknown variable.

Anahtar Kavram

Measures of Central Tendency
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Measures of Central Tendency

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