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The average age of a group of 8 members is 32 years ┬╖ If a new member aged 41 years joins the group, what will be the new average age of the group?
33 ┬аyears
34 ┬аyears
35 ┬аyears
32.5 ┬аyears
33 ┬аyears
Given: Initial number of members is 8 with an average age of 32 years ┬╖ A new member aged 41 years joins the group.
Initial number of members is 8 with an average age of 32 years ┬╖ A new member aged 41 years joins the group.
AveragenewтАЛ=n+1тИСxoldтАЛ+xnewтАЛтАЛ
Calculate the excess age beyond the old average: 41тИТ32=9. Distribute this excess among the new total of 8+1=9 members, adding 9├╖9=1 to the original average of 32 to get 33.
Students often add the new member's age to the total sum but forget to divide by the new count of members, i.e., 9 instead of 8.
Calculate the initial sum
Calculate the total age of the original 8 members by multiplying the count by the average.
Sum=8├Ч32=256
Calculate the new sum
Add the age of the new member to the total sum.
TotalSum=256+41=297
Determine the new count and average
Divide the new total sum by the new number of members (9).
AveragenewтАЛ=9297тАЛ=33
A is correct because the new total sum of 297 divided by 9 members results in an average of 33 years.
This deviation method is extremely useful in Data Interpretation sets where calculating large sums is time-consuming; always look for how much the new value deviates from the mean.