Question

The mean of 11 numbers is 35 if the mean of the first 6 numbers is 32 and another last six number 37 then the sixth number is

Answer 1

The answer is 29

Please refer the above photograph for the used process.



KEY POINTS TO REMEMBER :-

$sum = mean \times frequency$


SOLUTION :-



Given that :-
Mean of 11 numbers = 35
Mean of first 6 numbers = 32
Mean of last 6 numbers = 37

To find :- 6th observation

Solution :-

Sum of numbers = Mean * Number of observation.

So,
Sum of 11 numbers = 35*11 = 385

Sum of first 6 numbers = 32*6 = 196 .... (i)

Sum of last 6 numbers = 37*6 = 222 .... (ii)

Now,
Sum of (i) and (ii) = 222+192 = 414


Sixth observation = 414 - 385 = 29

Thus,
The 6th number is 29


Thanks!