Question

The mean of 2, 7, 6, x is 5 and mean of 18, 6, x, y is 10. What is the value of y?
a. 5
b. 10
c. 20
d. 30​

Answer 1

GIVEN :–

• The mean of 2, 7, 6, x is 5 .

• The mean of 18, 6, x, y is 10.

TO FIND :–

• Value of 'y' = ?

SOLUTION :–

• We know that mean –

$\\ \implies{ \boxed{ \bold{Mean = \dfrac{total \: \: sum}{total \: \: numbers} }}}$

• According to the first condition –

$\\ \implies{ \bold{5 = \dfrac{2 + 7 + 6 + x}{4} }}$

$\\ \implies{ \bold{5 = \dfrac{15+ x}{4} }}$

$\\ \implies{ \bold{5 = \dfrac{15+ x}{4} }}$

$\\ \implies{ \bold{20= {15+ x}}}$

$\\ \implies \large{ \boxed{ \bold{x = 5}}}$

• According to the second condition –

$\\ \implies{ \bold{10= \dfrac{18+ 6 + x + y}{4} }}$

• Put the value of 'x' –

$\\ \implies{ \bold{10= \dfrac{18+ 6 + 5+ y}{4} }}$

$\\ \implies{ \bold{40=29+ y}}$

$\\ \implies{ \bold{y = 40 - 29}}$

$\\ \implies \large{ \boxed{ \bold{y=11}}}$

Answer 2

Given ,

• The mean of 2 , 7 , 6 , x is 5 and mean of 18 , 6 , x , y is 10

First Condition :

The mean of 2 , 7 , 6 , x is 5

As we know that ,

$\boxed{ \sf{Mean = \frac{Sum \: of \: observation}{Number \: of \: observation} }}$

Thus ,

$\sf \mapsto 5 = \frac{2 + 7 + 6 + x}{4} \\ \\\sf \mapsto 20 = 15 + x \\ \\ \sf \mapsto x = 5$

$\therefore \underline{ \sf{The \: value \: of \: x \: is \: 10}}$

Second Condition :

The 18 , 6 , x , y is 10

Thus ,

$\sf \mapsto 10 = \frac{18 + 6 + x + y}{4} \\ \\\sf \mapsto 40 = 29 + y \: \: \: \{ \because x = 5 \} \\ \\\sf \mapsto y = 11$

$\therefore \underline{\sf{The \: value \: of \: y \: is \: 11}}$