Question

the average weight of a group of 75kg girls was calculated as 47kg. it was later discovered that the weight of one girl is 45kg. where is her actual weight was 25kg what is the actual average weight of the group of 75 girl {ROUNDED OFF TO TWO DIGIT AFTER DECIMAIL}
{A} 46.73
{B}46.64
{C}45.96
{D} CANNOT BE DITERMINED

Answer 1

Answer:

Given:

The average weight of a group of 75 girls = 47 kg

False reading, the weight of a girl = 45 kg

and actual reading of the weight of a girl = 25 kg

Formula used:

The average weight of persons = the total weight of persons/the number of persons

and the total weight of persons = average weight of persons × the number of persons

Calculation:

Wrong average weight = 47 kg

Total wrong weight = 47 × 75

⇒ total wrong weight = 3525 kg

Now the correct weight of 74 persons = 3525 –45

⇒ 3480 kg

Now total correct weight after including the correct weight of a girl = 3480 + 25

⇒ 3505 kg

The actual average weight of the group of 75 girls = 3505/75

⇒ 46.733 kg

∴ The actual average weight of the group of 75 girls is 46.73 kg.

Using weighted average method:

If the weight was considered 45 kg then the average was 47 kg

but instead of 45 kg, we have to take 25 kg as actual weight

so extra weight= 45-25 =20 kg

These 20 kgs need to be distributed among all and the result should be subtracted from the previous average.

so extra average weight = 20/75

⇒ 0.266 kg

Now an actual average weight = 47 - 0.266

⇒ 46.733 kg