Question

The average of 16 observations is 35. If 10 is multiplied to each observation, then the new average will be

Answer 1

Answer:  The new average is be 350.

Step-by-step explanation:  Given that the average of 16 observations is 35.

We are to find the average if 10 is multiplied to each observation.

Let a(1), a(2),  a(3),   .    .   .    ,    a(16) be the given 16 observations.

Then, according to the given information, we have

$\dfrac{a(1)+a(2)+a(3)+~~.~~.~~.~~+a(16)}{16}=35\\\\\\\Rightarrow a(1)+a(2)+a(3)+~~.~~.~~.~~+a(16)=35\times 16\\\\\Rightarrow a(1)+a(2)+a(3)~~.~~.~~.~~+a(16)=560~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Now, if 10 is multiplied to each observation, then the new average will be

$\dfrac{10a(1)+10a(2)+10a(3)+~~.~~.~~.~~+10a(16)}{16}\\\\\\=\dfrac{10}{16}\times \{a(1)+a(2)+a(3)+~~.~~.~~.~~+a(16)\}\\\\\\=\dfrac{10}{16}\times560~~~~~~~~[\textup{from equation (i)}]\\\\=10\times35\\\\=350.$

Thus, the new average is be 350.

Answer 2

Answer:

350

Step-by-step explanation:

Given  

The average of 16 observations is 35. If 10 is multiplied to each observation, then the new average will be

ANSWER

Given Average of 18 observations is 35

So if these observations is multiplied by 10, then the average will be 35 x 10 = 350.

Now the new average will be 350.

We can do it in another way.

a + b + c + d + e + f + g +…………..+ p / 16 = 35--------------(1)

Now each number is multiplied by 10.

So 10 a + 10 b + 10 c+ 10 d……10 p./16 = 10 (a + b + c + d +…………..+ p) / 16  

                                                            = 10 x 35 x 16 / 16

                                                           = 350

So new average will be 350.