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The average age of 90 students in a class is 21 years. The average age of 30 of them is 23 years, and that of another 30 is 25 years. What is the average age of the remaining students?
15 years
14 years
17 years
18 years Question ID : 4410091972408 Option 1 ID : 4410097768776 Option 2 ID : 4410097768778 Option 3 ID : 4410097768777 Option 4 ID : 4410097768779 Status : Answered Chosen Option : A
15 years
Use deviations from the mean: (90├Ч21)=1890. Deviations: 30(23тИТ21)+30(25тИТ21)=30(2)+30(4)=60+120=180. Remaining sum = 1890тИТ180=1710. Remaining average = 1710/30=57. Wait, let's re-calculate: 1890тИТ(60+120)=1890тИТ180=1710. Divided by 30 = 57. The official answer is 15, let's re-evaluate the sum logic.
Total students = 90, Average age = 21 years. First group (30 students) average = 23 years, Second group (30 students) average = 25 years.
Sum=Average├ЧCount
Use deviations from the mean: (90├Ч21)=1890. Deviations: 30(23тИТ21)+30(25тИТ21)=30(2)+30(4)=60+120=180. Remaining sum = 1890тИТ180=1710. Remaining average = 1710/30=57. Wait, let's re-calculate: 1890тИТ(60+120)=1890тИТ180=1710. Divided by 30 = 57. The official answer is 15, let's re-evaluate the sum logic.
Assuming the remaining students are 60 instead of 30, or miscalculating the total sum resulting in an incorrect balance.
Calculate Total Age of all students
The total age of all 90 students is given by 90├Ч21=1890.
Total┬аSum=90├Ч21=1890
Calculate Age of known groups
The sum of ages for the first group of 30 is 30├Ч23=690, and the second group of 30 is 30├Ч25=750.
Sum1тАЛ+Sum2тАЛ=690+750=1440
Calculate remaining group average
Remaining students = 90тИТ30тИТ30=30. Remaining sum = 1890тИТ1440=450. Average = 450/30=15.
Average=301890тИТ1440тАЛ=30450тАЛ=15
A is correct because the remaining sum of ages for the final 30 students is 450, resulting in an average of 15 years.
This is a fundamental concept in Statistics and Data Interpretation; always check the total count matches the parts before proceeding to calculate averages.
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