Here initial average = 7
As we know that, if all the numbers are multiple by a certain number, then their average must be a multiple of that number.
? New average = 7 x 12 = 84
Total of 6 observation = 6 x 12 = 72
Total of 7 observation (including the 7th) = 7 x (12 - 1) = 77
? 7th observation = 77 - 72 = 5
Required number = (Sum of all numbers) - [(Sum of first 5 numbers) + (Sum of last 3 numbers)
= 50 x 9 - ( 54 x 5 + 3 x 52)
= 450 - (270 + 156) = 450 - 426 ? 24
Average of all prime numbers between 60 and 90
= (61 + 67 + 71 + 73 + 79 + 83 + 89)/7
= 523/7 = 74.7
Required average = ( Sum of scores) / (No of scores)
= (124 + 856 + 331 + 227 + 963 + 338 + 259 + 662)/8
= 3760/8 = 470
Required average = (Sum of all scores) / (Number of scores)
= (235 + 124 + 255 + 534 + 836 + 375 + 101 + 433 + 760)/9
= 3681/9= 409
Total correct weight = (40 x 60) - 36 + 33 = 2400 - 3 = 2397 kg
? Required average weight = 2397/60 = 39.95 kg
Let the average of 14th innings = x
? Average of 15th innings = x+2
Then, 14x+72 = 15(x+2)
? 14x+72 = 15x +30
? x = 42
? Average for 15th innings = x+2 = 42 + 2 = 44
Total of 5 observations = 5 x 15 = 75
New sum = 75 + 16.5 + 18 + 14.5 = 124
New Average = 124 ? 8 = 15.5
x1 + x2 + x3 = 3 x 14 = 42 ....(i)
and (x1 + x2) x 2 = 30
? x1 + x2 =15 ....(ii)
From Eqs. (i) and (ii), we get
x1 + 15 = 42
? x1 = 42 - 15 = 27
Sum of the age of 45 students = 45 x 13 = 585 yr
Sum of the age of 15 students = 15 x18 = 270 yr
Sum of the age of all students = sum of the age of 45 students + sum of the age of 15 students
= 585 yr + 270 yr
=855 yr
? Average age of all students = 855 ? 60
= 14.25 yr
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