Question

The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x and also the value of the observation in the data.​

Answer 1

Given,

Set of observations = 6, 8, x+2, 10, 2x-1, 2

Mean of the observations = 9

To find,

Value of x and the value of observations with x.

Solution,

6, 8, x+2, 10, 2x-1, 2

Mean of the observations = 9

Mean = Sum of the observations/Total number of observations

Sum of observations = 6+8+(x+2)+10+(2x-1)+2

Sum of observations = 3x+27

Total number of observations = 6

Mean = $\frac{(3x+27)}{6} = 9$

$\frac{3(x+9)}{6} = 9$

$\frac{x+9}{2} = 9$

$x+9=18$

$x = 9$

3rd observation in the data = x+2

Substitute x=9, 9+2 = 11

4th observation in the data = 2x-1

Substitute x=9, 2(9)-1 = 17

Hence, value of x is 9 and the value of the observation in the data x+2 and 2x-1 are 11 and 17 respectively.