Question

If 8 is the mean of 4, 7, a, 8, 10, 12, find 'a'.
of 685 rand 4 is 7. find the
and 7​

Answer 1

Answer:

a=7

Step-by-step explanation:

Answer 2

• GIVEN:-

Mean = 8.

The numbers:- 4, 7, a, 8, 10, 12

• To Find:-

Value of 'a'.

• SOLUTION:-

Formula of mean =

$\large\boxed{\sf{\frac{sum\: of\: all\: observations}{total \:number \:of\: observations}}}$

Total no of observations = 6

According to the question,

$\large\Longrightarrow{\sf{Mean=\frac{sum\: of\: all\: observations}{total \:number \:of\: observations}}}$

$\large\Longrightarrow{\sf{8=\frac{4+7+a+8+10+12}{6}}}$

$\large\Longrightarrow{\sf{8=\frac{4+7+a+8+10+12}{6}}}$

$\large\Longrightarrow{\sf{8\times6=41+a}}$

$\large\Longrightarrow{\sf{48=41+a}}$

$\large\Longrightarrow{\sf{48-41=a}}$

$\large\therefore\boxed{\sf{a=7}}$

• Now let's verify it:-

$\large\Longrightarrow{\sf{Mean=\frac{sum\: of\: all\: observations}{total \:number \:of\: observations}}}$

Putting the value of a,

$\large\Longrightarrow{\sf{8=\frac{4+7+7+8+10+12}{6}}}$

$\large\Longrightarrow{\sf{8=\frac{48}{6}}}$

$\large\Longrightarrow{\sf{8=8}}$

$\large\therefore\boxed{\sf{LHS=RHS}}$

$\large\pink\therefore\boxed{\sf{\pink{Value\:of\:a=7}}}$