Average of 7 numbers is 28. One of these numbers is 22. 22 is replaced with a new number. New average becomes 30. What is that new number?
Given:
Initial average of 7 numbers = 28
Replaced number = 22
New average of 7 numbers = 30
Formula Used:
Sum = Average × Number of observations
Solution:
Initial total sum of the 7 numbers = 7 × 28 = 196
New total sum of the 7 numbers = 7 × 30 = 210
The increase in the total sum is due to the replacement of 22 with the new number.
Increase in sum = 210 - 196 = 14
Let the new number be x.
x - 22 = 14
x = 22 + 14
x = 36
Final Answer
So the correct answer is (b)
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