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Zorluk: OrtaMeasures of Central Tendency

A flight engineer is monitoring the fuel consumption, in gallons per hour (GPH), of a cargo aircraft during 44 different flight legs. The consumption for the first 33 legs was 520520, 480480, and 550550 GPH.

If the target mean fuel consumption for all 44 legs is 510510 GPH, what must the fuel consumption be for the 44 th leg?

  1. 490Cevap
  2. B
    500
  3. C
    515
  4. D
    530

Cevap

490
To find the missing value when given the mean, first determine the total sum required for all data points. Since the mean for 44 legs is 510510 GPH, the total fuel consumption must be 4×510=20404 \times 510 = 2040 GPH. The sum of the first three legs is 520+480+550=1550520 + 480 + 550 = 1550 GPH. Subtracting this sum from the required total gives the fuel consumption required for the fourth leg: 2040−1550=4902040 - 1550 = 490 GPH.

Adım Adım Çözüm

1
Set up the formula for the mean of 44 flight legs.
520+480+550+x4=510\frac{520 + 480 + 550 + x}{4} = 510
The mean is calculated by dividing the sum of all values by the total number of values.
2
Calculate the total target fuel consumption required for all 44 legs.
510×4=2040510 \times 4 = 2040
Multiplying the target mean by the total number of legs gives the required overall sum.
3
Calculate the sum of the fuel consumption for the first 33 legs.
520+480+550=1550520 + 480 + 550 = 1550
This represents the total fuel consumed so far.
4
Subtract the sum of the first 33 legs from the total target consumption to find the missing value.
2040−1550=4902040 - 1550 = 490
The difference between the required total and the current total must be the consumption of the 44 th leg.

Anahtar Kavram

Calculating a missing value when given the mean
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Konular

Measures of Central Tendency

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