While calculating the weight of a group of men, the weight of 63 kg of one member was...
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While calculating the weight of a group of men, the weight of 63 kg of one member was mistakenly written as 83 kg. Due to this the average of the weights increased by half kg. What is the number of men in the group?
Show answer & explanation
The error introduced is 83 - 63 = 20 kg. This error is distributed across all n members, so the average increases by 20/n kg. Setting 20/n = 0.5 and solving gives n = 40 men in the group.
Step-by-step Derivation:
Let n = number of men in the group.
When 63 kg is mistakenly recorded as 83 kg:
- Error magnitude = 83 - 63 = 20 kg (amount overstated)
- This error is distributed across n members when calculating average
- Average increase = Total error / Number of members
Set up equation:
20 / n = 0.5
Solve for n:
20 = 0.5n
n = 20 / 0.5
n = 40
Verification: If the total weight increased by 20 kg and this caused the average to increase by 0.5 kg, then 20 ÷ 0.5 = 40 members. ✓