Question

The average of 7 numbers is48 .if two of them are 60 and 56 what is the average of the other five numbers.

Answer 1

Answer:

Find the sum of the 7 numbers:

Average = 48

Sum = 48 x 7 = 336

Find the sum of the 5 numbers:

Sum = 336 - 56 - 60 = 220

Find the average of the 5 numbers:

Average = Total ÷ Number of numbers

Average = 220 ÷ 5 = 44

Answer = The average of fibe number is = 44

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Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that the 7 observations be

$\rm \: x_1, \: x_2, \: x_3, \: x_4, \: x_5, \: x_6, \: x_7 \:$

Such that

$\rm \: \: x_6 = 60$

and

$\rm \: \: x_7 = 56$

Now, it is given that

The average of 7 numbers is 48.

We know that

$\boxed{\rm{  \:Average = \frac{Sum \: of \: observatons}{Number \: of \: observations} \: }}$

So, on substituting the values, we get

$\rm \: Average = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7}{7}$

$\rm \: 48 = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + 60 + 56}{7}$

$\rm \: 48 = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 +116}{7}$

$\rm \: x_1 + x_2 + x_3 + x_4 + x_5 + 116 = 336$

$\rm \: x_1 + x_2 + x_3 + x_4 + x_5 = 336 - 116$

$\rm \: x_1 + x_2 + x_3 + x_4 + x_5 = 220$

Now, we have to find the average of remaining numbers.

So,

$\rm \: Average = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5}{5}$

$\rm \: Average = \dfrac{220}{5}$

$\rm\implies \:\boxed{\rm{  \:Average \: = \: 44 \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

1. If each observation is increased by any constant real number k, mean is also increased by k.

2. If each observation is decreased by any constant real number k, mean is also decreased by k.

3. If each observation is multiplied by any non - zero constant real number k, mean is also multiplied by k.

4. The sum of deviations taken from mean is always zero.