Question

118. The mean marks obtained by 300 students in the subject of statistics is 45. The mean
marks of the top 100 of them was found to be 70 and the mean of last 100 was known to
be 20. What is the mean of the remaining 100 students.
(2) 57.5
(3) 50
(4) 65
(1) 45​

Answer 1

let x1,x2,x3.........x300 be the students

total mean =(x1+x2+x3+.............x300)/300=45

then x1+x2+x3+............+x300=300*45--------------->equn1

mean of first 100 students is=(x1+x2+x3.........+x100)/100=70

then x1+x2+x3+........+x100=7000

mean of last 100 students is =(x201+x202+x203+.............+x300)/100=20

then x201+x202+x203+.........x300=2000

finally by substituting the values in equn1 we get

7000+(x101+x102+x103+...........+x200)+2000=300*45

x101+x102+..........+x200=13500-9000=4500

avg of remaining 100 students =(x101+x102+..........+x200)/100=4500/100=45

FINAL ANSWER =45