The average weight of a group of 75 girls was calculated as 47 kg. It was later discovered that the weight of one of the girls was read as 45 kg, whereas her actual weight was 25 kg. What is the actual average weight of the group of 75 girls?

Given:

Total number of girls = 75

Average weight of 75 girls = 47 kg

To find: We have to the actual average weight of the group of 75 girls.

Solution: 

Now,

$Average\ weight\ of\ all\ girls\ =\ \frac{Sum\ of\ weight\ of\ all\ girls\ }{Total\ number\ of\ girls}$

$\Longrightarrow \ 47\ =\ \frac{Sum\ of\ weight\ of\ all\ girls\ }{75}$

$\Longrightarrow \ Sum\ of\ weight\ of\ all\ girls\ =\ 75\ x\ 47\ =\ 3525$

Now, given that one of the gir| was read as 45 kg, whereas her actual weight was 25 kg, which means 45 is subtracted from this sum and 25 is added,

Actual sum of all weights = 3525 - 45 + 25 = 3505

Calculating actual average by dividing actual weight by number of girls:

=> $Average\ weight\ of\ all\ girls\ =\ \frac{Sum\ of\ weight\ of\ all\ girls\ }{Total\ number\ of\ girls}$

=> $Average\ weight\ of\ all\ girls\ =\ \frac{3505\ }{75}$

=> Actual average weight = 46.73

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Updated on: 10-Oct-2022

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