Question

The mean of 13 observation is 14. If the mean of the first 7 observations is 12 and that of the last 7 observation is 16 then find the 7th observation...........

pls give the process to find this answer...

pls pls​

Answer 1

Answer:

14

Step-by-step explanation:

You calculate the sum of all 13 observations by multiplying the mean by 13 i.e 13 X 14 = 182

Then you calculate the sum of first 7 observations by multiplying the mean of first 7 observations by 7 i.e. 12 X 7 = 84

Then you calculate the sum of last 7 observations(n7 to n13) by multiplying the mean of first 7 observations by 7 i.e. 16 X 7 = 112

Now if you add 84 + 112 = 196, it will contain 2 X n7 + (n1+n2+...+n6) + (n8+...+n13). This is because n7 occurs in both first 7 and last 7 observations.

Then we subtract 196 - 182 = 14. This is because in 196 all numbers except n7 are present once and n7 is present twice but in 182 all numbers are present once. So, everything will be cancelled except one n7 which will have the value 14