Question

if the average of k numbers is z. if the each number is trippled the new average is ​

Answer 1

SOLUTION

GIVEN

The average of k numbers is z.

TO DETERMINE

If each number is tripled the new average

EVALUATION

Let the given k numbers are

$\sf{x_1, x_2, x_3,..., x_k}$

Now it is given that the average of k numbers is z

$\displaystyle \sf{z = \frac{ \sf{x_1 + x_2 + x_3 + ... + x_k}}{k} }$

Now each number is tripled

So the new numbers are

$\sf{3x_1, 3x_2, 3x_3,..., 3x_k}$

Hence the required average

$\displaystyle \sf{= \frac{ \sf{3x_1 + 3x_2 + 3x_3 + ... + 3x_k}}{k} }$

$\displaystyle \sf{= \frac{ \sf{3(x_1 + x_2 + x_3 + ... + x_k)}}{k} }$

$\displaystyle \sf{= 3 \times z }$

$\displaystyle \sf{= 3z }$

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