Question

37,45,x,28,41,26,33,38,40 if mean is 13.6 find value of x​

Answer 1

★ How to do :-

Here, we are given with nine observations and the mean value of that data. But, we aren't given with the value of one observation in that data. That observation is represented by a variable x. We are asked to find the value of that same variable x. To find the value of x in this data, we use the formula that is used to calculate the mean. We substitute the values of all the data in the numerator and the the number of total observations in the given data in the denominator. This is the formula to calculate the mean. The obtained fraction to us is as equal to the value of mean i.e, 13.6. We then find the value of x by transposition method in which we shift the numbers from one hand side to the other. So, let's solve!!

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➤ Solution :-

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

Substitute the given values.

${\sf \leadsto 13.6 = \dfrac{37 + 45 + x + 28 + 41 + 26 + 33 + 38 + 40}{9}}$

Add four numbers together each in the numerator.

${\sf \leadsto 13.6 = \dfrac{151 + x + 137}{9}}$

Add the remaining two numbers in the numerator.

${\sf \leadsto 13.6 = \dfrac{288 + x}{9}}$

Shift the number 9 from LHS to RHS.

${\sf \leadsto 13.6 \times 9 = 288 + x}$

Multiply the values on LHS.

${\sf \leadsto 122.4 = 288 + x}$

Shift the number 288 from LHS to RHS, changing it's sign.

${\sf \leadsto x = 122.4 - 288}$

Subtract the values to get the value of x.

${\sf \leadsto x = -165.6}$

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${\red{\underline{\boxed{\bf So, \: the \: value \: of \: x \: is \: (-165.6).}}}}$

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Verification :-

${\sf \leadsto 13.6 = \dfrac{37 + 45 + x + 28 + 41 + 26 + 33 + 38 + 40}{9}}$

Substitute the value of x.

${\sf \leadsto 13.6 = \dfrac{37 + 45 + (-165.6) + 28 + 41 + 26 + 33 + 38 + 40}{9}}$

Add all the numbers on the numerator.

${\sf \leadsto 13.6 = \dfrac{82 - 165.6 +206}{9}}$

Add and subtract the remaining numbers.

${\sf \leadsto 13.6 = \dfrac{122.4}{9}}$

Simplify the fraction to get the value of RHS.

${\sf \leadsto 13.6 = 13.6}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!