Question

The average of 10 numbers is 15.34. the average of the first five numbers is 14.35 and the average of the last 6 numbers is 15.43. if the fifth number is wrong, find the average of the other numbers.

Answer 1

(a1 + a2 + ... + a10)/10 = 15.34
a1 + a2 + ... +a10 = 153.4   ...(1)
Similarly,
a1 + a2 + ... + a5 = 71.75   ...(2)
a5 + a6 + ... + a10 = 92.58   .(3)
If you subtract 2 from 1, you get
a6 + a7 + ... + a10 = 81.65   ...(4)
similarly if you subtract 3 from 1, you get
a1 + a2 + .. + a4 = 60.82   ...(5)

Taking average of 4 and 5,
a1 + a2 + ... + a4 + a6 + ... + a10  = 142.97
Dividing above equation with 9 on both sides,
Average of other numbers = 15.83