Question

The mean of 10 numbers is 12.5 . The mean of first six numbers is 15 and the mean of last five numbers is 10. Find the sixth number.

Answer 1

(Question incorrect, 6+5=11≠10)
Mean of 1st 10 numbers=12.5
Mean of 1st 6 numbers=15
Also, mean of 5numbers=10
Total of 10 observations=125(12.5×10)
And total of 6=90
Also total of 5 numbers= 50
=90+40=140≠125
What is this?
The question is incorrect.

Answer 2

let the numbers are a1, a2, a3, a4, a5, a6, a7, a8, a9, a10.
mean of 10 numbers = 12.5
total of 10 numbers = 12.5*10 = 125(a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10)
mean of 6 numbers = 15
total of 6 numbers = 15*6 = 90(a1 + a2 + a3 + a4 + a5 + a6). ....(i)
mean of last 5 numbers = 10
total of last 5 numbers = 10*5 = 50(a6 + a7 + a8 + a9 + a10). .......(ii)

adding (i) and (ii)
a1 + a2 + a3 + a4 + a5 + a6 + a6 + a7 + a8 + a9 + a10 = 90+50
(a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10) + a6 = 140
125 + a6 = 140
a6 = 140 - 125
Thus, a6 = 15
Hence, the vi number is 15.


I know it's been quite late but let it be in here for other students.