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The mean of five numbers is 20. If one number is excluded, the mean of the remaining four numbers becomes 18. What is the excluded number?
28
25
30
22
28
Calculate the change in mean (20тИТ18=2) and multiply by the remaining count (4), then add the new mean (18+(2├Ч4)=26 is incorrect; rather: original mean + change ├Ч remaining = 20+(2├Ч4)=28).
Mean of five numbers is 20, and mean of the remaining four numbers after excluding one is 18.
Sum=Mean├ЧCount
Calculate the change in mean (20тИТ18=2) and multiply by the remaining count (4), then add the new mean (18+(2├Ч4)=26 is incorrect; rather: original mean + change ├Ч remaining = 20+(2├Ч4)=28).
Students often subtract the new sum from the original sum but miscount the number of items remaining or forget that the excluded number contributes to the original mean.
Calculate original sum
The sum of the five numbers is calculated by multiplying the mean by the count of numbers.
S1тАЛ=20├Ч5=100
Calculate new sum
After excluding one number, the count becomes 4 and the mean is 18. The new sum is calculated accordingly.
S2тАЛ=18├Ч4=72
Find the excluded number
The excluded number is the difference between the original sum and the new sum.
Excluded┬аNumber=S1тАЛтИТS2тАЛ=100тИТ72=28
A is correct because the difference between the sum of 5 numbers (100) and the sum of 4 numbers (72) is 28.
This concept of 'sum adjustment' is fundamental for questions involving 'replacement of members' in groups, a common topic in Data Interpretation and Average-based aptitude tests.