Question

The average weight of a sample of 10 apples is 52 g. later it was found that the weighing machine had shown the weight of each apple 10 g less. The correct average weight of an apple is
A 62 g
B 54 g
C 56 g
D 52 g

Answer 1

Hint: Average weight of any given quantities is the ratio of sum of the weight of given quantities to the number of quantities. Average of any given quantities shows the central term of that group or quantities.

Complete step-by-step answer:
Given: sample of 10 apples and the average weight of 10 apples is 52 kg.
Error found in the weight of each apple is 10 g.
Weight of 10 apples$ = 52 \times 10 = 520\,{\rm{kg}}$
It is given that the weighing machine showed the weight of each apple 10 gram less than its original weight. So the error occurs in showing weight of 10 apples,
${l}
 = 10 \times 10\\
 = 100\,{\rm{g}}
$
Now we can calculate the actual weight of apples by adding the given weight for 10 apples and error occurred in their weight,
${l}
 = 520 + 100\\
 = 620\,{\rm{g}}
$
Average weight of apples is determined by dividing the actual weight of apples from the total number of apples.
Average weight of apples,
${l}
 = \dfrac{{620}}{{10}}\\
 = 62\,{\rm{g}}
$
Thus the actual average weight of 10 apples is 62 g and the correct option for the solution is (A).

Note: Students might make mistakes in adding the error that occurred in weight. So remember that the machine shows 10 g less for each apple it means we have to add that weight for calculating the actual average weight of apples.