Question

The average of eight numbers is 20. If one number 15 of them is replaced by 31, then the average will be

Answer 1

Average = Sum of eight numbers / Total numbers

Therefore
20 = n1 + n2 + n3 +n4 + n5 + n6 + n7 + n8 / 8

20 = n1 + n2 + n3 +n4 + n5 + n6 + n7 + 15 / 8

160 = n1 + n2 + n3 +n4 + n5 + n6 + n7 + 15

160 - 15 = n1 + n2 + n3 +n4 + n5 + n6 + n7

145 = n1 + n2 + n3 +n4 + n5 + n6 + n7 ...(1)

Now if one number is 31 then

Average = n1 + n2 + n3 +n4 + n5 + n6 + n7 + 31 / 8

= 145 + 31 /8 ( from ..(1) )

= 176 / 8

= 22