The average of 100 numbers was wrongly calculated to be 75 because a number 100 was wrongly counted as 50. What is the correct average of these numbers?
Answers
Total Number = 100
average = 75
Sum of numbers = 100×75
Wrong number value=50, Correct number value=100
∴Correct sum=100×75-50+100
=100×75+50
=7550
Correct average = 7550/100
=75.50
Given:
Wrong average=75
To find:
The correct average
Solution:
The correct average is 75.5.
We can obtain the correct average required by subtracting the wrong value taken and adding the right value to the numbers' sum.
The average of the given numbers=Sum of all numbers/ total numbers
Using the values,
75=Sum of 100 numbers/100
75×100=Sum of 100 numbers
Sum of 100 numbers=7,500
Now, the wrong value will be subtracted and the right value will be added to the sum.
The correct average=(Sum of 100 numbers-50+100)/100
=(7,500+50)/100
=7550/100
=75.5
Therefore, the correct average is 75.5.