Question

The average weight of 10 objects is 45 kg. If another object of weight 56 kg is added, then the average weight of the 11 objects, is

• A. 47
• B. 46
• C. 48
• D. 49

Hint:

Alternative Deviation Method: The new object adds an extra \(56 - 45 = 11 \text{ kg}\) above the old average. Distributing this surplus of 11 kg equally among all 11 objects adds \(11 \div 11 = 1 \text{ kg}\) to the original average: \[ \text{New Average} = 45 + 1 = 46 \text{ kg} \]

Answer 1

The Correct Option is B

Concept: The statistical mean or average value of a given set containing \(n\) individual data items is defined as the sum of all elements divided by the total number of entries: \[ \text{Average} = \frac{\text{Sum of all elements}}{\text{Total number of elements } (n)} \] This relationship allows us to compute the total combined weight using: \[ \text{Sum of elements} = \text{Average} \times n \]

Step 1: Calculate the total combined weight of the initial 10 objects.
We are given:
• Number of initial items (\(n_1\)) = 10 objects
• Initial average weight = 45 kg Using the product formula to find the total sum of their weights: \[ \text{Initial Sum} = 10 \times 45 = 450 \text{ kg} \]

Step 2: Update the sum and the count with the new object.
A new single object weighing 56 kg is introduced into the set. \[ \text{New Combined Sum} = \text{Initial Sum} + \text{Weight of the new object} \] \[ \text{New Combined Sum} = 450 + 56 = 506 \text{ kg} \] The new total count of objects in the collection is: \[ \text{New Count } (n_2) = 10 + 1 = 11 \text{ objects} \]

Step 3: Compute the new updated average weight.
Divide the new combined weight sum by the total number of objects: \[ \text{New Average} = \frac{\text{New Combined Sum}}{\text{New Count}} = \frac{506}{11} \] Let us perform the long division: \[ 50 \div 11 = 4 \text{ with a remainder of } 6 \quad (\text{since } 4 \times 11 = 44) \] Bring down the remaining digit 6 to form 66: \[ 66 \div 11 = 6 \quad (\text{since } 6 \times 11 = 66) \] \[ \text{New Average} = 46 \text{ kg} \] The new average weight of the 11 objects is 46 kg, matching Option (B).