Question

. The average of 20 values is 18. If 3 is
subtracted from each of the values, then the
new average will be
(1) 21
(2) 15
(3) 16
(4) 17​

Answer 1

Answer :-

$\leadsto \: \boxed{ \sf{ \red{(2) \: \: 15}}}$

Step-by-step explanation:

To Find :-

• The new average

Solution:

Given that,

• The average of 20 values = 18
• 3 is subtracted from each of the values

Therefore,

$\sf{\large{\underline{Assumption}}}$

• Let the sum of 20 values = x

Now, As we know that,

$\boxed{\red{\tt{Average = \dfrac{Sum \: of \: all \: observations}{Total \: number \: of \: observations}}}}$

Therefore,

$\longrightarrow \: \sf{18 = \dfrac{x}{20}}$

By Flipping both sides,

$\longrightarrow \: \sf{ \dfrac{x}{20} = 18}$

By cross multiplication,

$\longrightarrow \: \sf{x = 18 \times 20}$

By multiplying,

$\longrightarrow \: \sf{x = 360}$

As given, subtracting 3 from each of the values :-

So,

$\longrightarrow \: \sf{value \times 3}$

$\longrightarrow \: \sf{20 \times 3}$

By multiplying,

$\longrightarrow \: \sf{60}$

Now, subtracting 60 from 360,

$\longrightarrow \: \sf{360 - 60}$

By subtracting,

$\longrightarrow \: \sf{300}$

Therefore, the new average value is :-

As we know that,

$\boxed{\red{\tt{Average = \dfrac{Sum \: of \: all \: observations}{Total \: number \: of \: observations}}}}$

By the question,

$\longrightarrow \: \sf{Average = \dfrac{300}{20}}$

By dividing, 300 with 20,

$\longrightarrow \: \sf{Average = 15}$

Hence,

The required number is $\boxed{\sf{\red{15}}}$.