Question

if the mean of of five observation x,x+4,x+6,x+8and x+12 is 16 find the value of x?​

Answer 1

$\sf{Answer}$

Step-by-step-explanation:-

Given :-

• Observations are x , x+4 , x+6 , x+8 , x+12
• Mean of observations is 16

To find :-

Value of x

Formula implemented:-

Mean = $\sf\dfrac{Sum\: of\: observations}{No\:of\: observations}$

Lets do !

Sum of observations = x + ( x + 4) + (x+6) + (x + 8) + ( x + 12)

Remove brackets

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

Keep x terms aside & numbers aside

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

5x + 30

Sum of observations = 5x + 30

No.of observations = 5

Mean = 16

But we know mean = $\sf\dfrac{Sum\:of \:observations}{No.of \:observations}$

∴ 16 = $\sf\dfrac{Sum\: of\: observations}{No.of\: observations}$

16 = $\sf\dfrac{5x+30}{5}$

Do cross multiplication

16 (5) = 5x + 30

80 = 5x + 30

Transpose 30 to LHS

80 - 30 = 5x

50 = 5x

x = 50/5

x = 10

Finding observations :-

x = 10

x + 4 = 10+4

x + 4 = 14

x + 6 = 10 + 6

x + 6 = 16

x + 8 = 10+8

x + 8 = 18

x + 12 = 10 + 12

x + 12 = 22

So, the observations are 10, 14 , 16, 18 , 22

Value of x is 10