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Difficulty: MediumMeasures of Central Tendency for Ungrouped Data

The mean mass of 66 packages in a delivery van is 20 kg20\text{ kg}. If one package weighing 35 kg35\text{ kg} is unloaded from the van, what is the mean mass of the remaining 55 packages?

  1. 17 kg17\text{ kg}Answer
  2. B
    23 kg23\text{ kg}
  3. C
    31 kg31\text{ kg}
  4. D
    14 kg14\text{ kg}

Answer

The mean mass of the remaining packages is 17 kg17\text{ kg}.
The total weight of the initial 66 packages is 6×20 kg=120 kg6 \times 20\text{ kg} = 120\text{ kg}. Unloading one package of 35 kg35\text{ kg} leaves 120−35=85 kg120 - 35 = 85\text{ kg}. Dividing this remaining mass by the remaining 55 packages yields 855=17 kg\frac{85}{5} = 17\text{ kg}.

Step-by-Step Solution

1
Calculate the initial total mass of the 6 packages
Total mass=6×20=120 kg\text{Total mass} = 6 \times 20 = 120\text{ kg}
The sum of a set of numbers is equal to the product of their count and their mean.
2
Calculate the total mass after unloading the 35 kg package
New total mass=120−35=85 kg\text{New total mass} = 120 - 35 = 85\text{ kg}
Removing a package decreases the total combined mass by its individual weight.
3
Calculate the new mean mass for the remaining 5 packages
New mean=855=17 kg\text{New mean} = \frac{85}{5} = 17\text{ kg}
The mean of ungrouped data is found by dividing the new sum by the updated count of items (6−1=56 - 1 = 5).

Key Concept

Calculation of the mean of ungrouped data after removing an item
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Topics

Measures of Central Tendency for Ungrouped Data

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