Question

If the mean of five observations x, x+4, x + 6, x + 8 and x + 12 is 16, find the value of x.​

Answer 1

Step-by-step explanation:

Given:-

the mean of five observations x, x+4,

x + 6, x + 8 and x + 12 is 16.

To find:-

Find the value of x.

Solution:-

Given that

Given observations are:

x , x+4 , x+6 , x+8 , x+12

Number of observations = 5

Sum of all observations

=>x + x+4 + x+6 + x+8 + x+12

=>5x + 30

Mean = Sum of all observations/Number of all observations

=>Mean = (5x+30)/5

=>Mean = 5(x+6)/5

=>Mean = x+6

According to the given problem

Mean of the given observations = 16

=>x+6 = 16

=>x = 16-6

=>x = 10

Therefore,x=10

Answer:-

The value of x for the given problem is 10

Used formula:-

• Mean = Sum of all observations/Number of all observations

Check:-

If x = 10 then the given observations are

10,14,16,18,22

Sum of all observations =

10+14+16+18+22=80

Number of all observations = 5

Mean = 80/5 = 16

Verified the given relation