Question

8
The Arithmetic mean of 1,3,4,7,9, X,
15 is 7 the value of Xis
(1 Point)​

Answer 1

Given :

• Arithmetic mean of 1,3,4,7,9, X, 15 = 7

To find :

• the value of X

Formula used :

$arithmetic \: \: mean = \dfrac{sum \: of \: terms}{number \: of \: terms}$

Solution :

Arithmetic mean of 1,3,4,7,9, X, 15 = 7.

Now to find the value of x we will use the given formula :-

$\implies \: arithmetic \: \: mean = \dfrac{sum \: of \: terms}{number \: of \: terms}$

sum of term : 1+3+4+7+9+X+15

Number of terms = 7

$\implies \: arithmetic \: \: mean = \dfrac{1 + 3 + 4 + 7 + 9 + x + 15}{7}$

put arithmetic mean = 7

$\implies7= \dfrac{1 + 3 + 4 + 7 + 9 + x + 15}{7}$

$\implies7= \dfrac{39 + x }{7}$

Now cross multiply :-

$\implies7 \times 7= {39 + x }$

$\implies49= {39 + x }$

$\implies49 - 39= { x }$

$\implies10= { x }$

Therefore the value of x = 10

Answer : 10

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Verification of Answer :-

To verify our answer we will put x = 10 in 1,3,4,7,9, X, 15 and then find mean. If we get mean of these terms as 7 then the answer is correct.

$\implies \: arithmetic \: \: mean = \dfrac{sum \: of \: terms}{number \: of \: terms}$

$\implies \: arithmetic \: \: mean = \dfrac{1 + 3 + 4 + 7 + 9 + 10 + 15}{7}$

1 + 3 + 4 + 7 + 9 + 10 + 15 = 49

$\implies \: arithmetic \: \: mean = \dfrac{4 9 }{7}$

$\implies \: arithmetic \: \: mean = {7}$

Hence verified

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