Question

The arithmetic mean of five numbers is 8, one item 15 is replaced by 5, what
is the new arithmetic mean
​

Answer 1

Answer:

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Step-by-step explanation:

Mean of 10 number is 20.

Sum of 10 numbers = 200

When each number is multiplied by 2 and 5 is added to each number, new sum = 2×200+10×5=450

Now, new mean =  

10

450

​  

=45

Answer 2

Answer:

We have the arithmetic mean of five numbers is $8$. Now one number is replaced by another number. So we should find the new arithmetic mean.

Final Answer: New arithmetic mean: $6$

Step-by-step explanation:

We consider that five numbers are, $x_{1}, x_{2},x_{3},x_{4},x_{5}$. But we know the one number $15$. Their arithmetic mean $=8$.

Formula for arithmetic mean $=\frac{sum of the given numbers}{number of values}$

That is,      arithmetic mean   $=\frac{x_{1}+x_{2}+x_{3}+x_{4}+x_{5}}{5}$

Already we know, $x_{5} =15$. arithmetic mean $=8$. Now apply this value in the above equation.

That is,           $\frac{x_{1}+x_{2}+x_{3}+x_{4}+15}{5}=8$

           $x_{1}+x_{2}+x_{3}+x_{4}+15=40$

                   $x_{1}+x_{2}+x_{3}+x_{4}=40-15$

                   $x_{1}+x_{2}+x_{3}+x_{4}=25$  ----------------------(1)

Now that number $x_{5} =15$ is replaced by $5$. New arithmetic mean = ?

For that we should use the same formula. New arithmetic mean is considered as $x$.

That is,              $\frac{x_{1}+x_{2}+x_{3}+x_{4}+5}{5}=x$  

              $x_{1}+x_{2}+x_{3}+x_{4}+5=5x$

Substitute equation(1) in the above equation.

                                      $25+5=5x$   ⇒ ($x_{1}+x_{2}+x_{3}+x_{4}=25$)

                                             $5x=25+5$

                                             $5x=30$

                                               $x=\frac{30}{5}$

         New arithmetic mean $x=6$