Question

the average of 6 positive number is 6 if the average of the least and the greatest of these number is 8 what is the average of the other 4 numbers​

Answer 1

QUESTION :-

The average of 6 positive number is 6 if the average of the least and the greatest of these number is 8 what is the average of the other 4 numbers

Answer :-

Let the 6 numbers be :- x,y,z,a,b,c respectively.

According to the question,

Average of the 6 numbers = 6

Average of the least and the greatest number = 8

To find :-

The average of the remaining 4 numbers.

$\dfrac{x + y + z + a + b + c}{6} = 6$

Let us assume x to be the greatest number and y to be the least.

The average of x and y is 8 (given)

$\dfrac{x + y}{2} = 8$

By transposing 2 to the other side,

$x + y = 8 \times 2 = > 16$

Now that we know the value of x + y, let us substitute this value in the initial average.

$\dfrac{16 + z + a + b + c}{6} = 6$

Transposing 6 to the other side,

$16 + z + a + b + c = 6 \times 6$

$16 + z + a + b + c = 36$

Transposing 16 to the LHS(Left Hand Side) now,

$z + a + b + c = 36 - 16$

$z + a + b + c = 20$

We know that :-

$average = \dfrac{sum \: of \: the \: observations}{total \: number \: of \: observations}$

Now that we have the sum of the remaining 4 numbers, the average will be :-

$average = \dfrac{20}{4}$

$= > 5$

Therefore the average of the 4 numbers is 5.