Question

10-if the mean of 16, 14, X, 23, 20 is 18. Find the
value of x.
a. 17
b-16​

Answer 1

Answer :-

• Option a is correct.

• The value of x is 17.

Given :-

• The mean of 16, 14, x, 23 and 20 is 18.

To find :-

• The value of x.

Step-by-step explanation :-

We know that :-

$\underline{ \boxed{ \sf Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations}}}$

Here,

• Sum of observations = 16 + 14 + x + 23 + 20.

• Number of observations = 5.

• Mean = 18.

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$\underline{\underline{\mathfrak{Substituting \: these \: values \: in \: the \: formula,}}}$

$\boxed{\sf \dfrac{16 + 14 + x + 23 + 20}{5} = 18}$

Adding all the numbers,

$\implies\boxed{ \sf\dfrac{73 + x}{5} = 18}$

Transposing 5 from LHS to RHS, changing it's sign,

$\implies\boxed{ \sf73 +x = 18 \times 5}$

On multiplying 18 by 5,

$\implies \boxed {\sf73 + x = 90}$

Transposing 73 from LHS to RHS, changing it's sign,

$\implies\boxed{ \sf x = 90 - 73}$

Subtracting 73 from 90,

$\implies \overline{\boxed{\sf x = 17.}}$

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• Hence, the value of x is 17.

Answer 2

★ Question :-

• If the mean of 16, 14, x , 23, 20 is 18.Find the value of x.

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★ Given :-

• Mean of 16, 14, x, 23, 20 is 18.

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★ To find :-

• value of x

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★ Formula to remember :-

$\large {\boxed {\pmb {\sf {\underline {\overline {\red { Mean \; = \dfrac{ sum \; of \; observations}{Total \; observations}}}}}}}}$

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★ Solution :

• Mean = 18
• Sum of observations = 16 , 14, x, 23, 20
• Total observations = 5

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$\small {\pmb {\frak {\underline {\pink {Putting \; the \; values \; in \; formula :-}}}}}$

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$\to \sf { 18 = \dfrac { 16 + 14 + x + 23 + 20}{5}}$

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$\to \sf { 18 = \dfrac { 73 + x}{5}}$

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$\to \sf { 18 \times 5 = 73 + x}$

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$\to \sf { 90 = 73 + x}$

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$\to \sf { 90 - 73 = x}$

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$\to \sf { 17 = x}$

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⋆ So, the value of x = 17.

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❖ Therefore, Opt (a) is correct.