Problem: The arithmetic mean of a set of 50 numbers is 38. If two numbers of the set, namely 45 and 55, are discarded, the arithmetic mean of the remaining set of numbers is:
Answer Choices:
A. 38.5
B. 37.5
C. 37
D. 36.5
E. 36
Solution:
Since the arithmetic mean of the 50 numbers is 38 , the total of the 50 numbers is 50×38=1900. Removing the two numbers 45 and 55 leaves 48 numbers with a total of 1800 . Therefore, the new arithmetic mean =481800=37.5
or
a1+a2+⋯+a48+100=50⋅38=50(36⋅2)=50⋅36+50⋅2.
∴a1+a2+⋯+a48=50⋅36=48 A.M.(new). ∴A.M.( new )=4850⋅36=37.5