Question

2. If the mean of the following observations is 39, find the value of x. 29, 48, x, 51, x-3.​

Answer 1

☯GIVEN :

• Mean of the given observations = 39

• Observations : 29 , 48 , x , 51 , x-3

☯TO FIND :

• The value of x.

☯FORMULA REQUIRED :

$\underline{\boxed{ \red {\bf{Mean = \dfrac{Total \: sum \: of \: observations}{Total \: number \: of \: observations}}}}}$

➲SOLUTION :

• Mean of the given observations = 39

$\implies{\sf{Mean = \dfrac{Total \: sum \: of \: observations}{Total \: number \: of \: observations}}}$

$\implies{\sf{39= \dfrac{29 + 48 + x + 51 + (x - 3)}{5}}}$

$\implies{\sf{39= \dfrac{29 + 48 + x + 51 + x - 3}{5}}}$

$\implies{\sf{39= \dfrac{125 +2x }{5}}}$

• By cross multiplication :

$\implies{\sf{39 \times 5= 125 + 2x}}$

$\implies{\sf{195= 125 + 2x}}$

• Transposing 125 to the left side :

$\implies{\sf{195 - 125 = 2x}}$

$\implies{\sf{70 = 2x}}$

• Dividing both sides by 2 :

$\implies{\sf{ \cancel{ \dfrac{70}{2}} = x}}$

• After dividing both sides by 2 :

$\implies{\sf{35 = x}}$

$\implies{ \underline{\huge {\boxed{\pink{\bf{ x = 35}}}}}}$

$\huge{\red{\therefore}}$The value of x is 35.