Question

The average of 8, 9, 12, 16 and p is 11
find the value of p​

Answer 1

★ How to do :-

Here, we are given with some of the numbers and one of them isn't given which is replaced by a variable p. We are also given with the average of those all numbers. We should find the value of the variable p by the formula of average. We can substitute the value of average in it's place and the given data on the numerators and the number of observations in the denominator. Then, we can find the value of p by the concept of transposition method. We can first add the given observations and then, we can shift the the denominator from LHS to RHS. This method is classified as the transposition method. The sign of that number changes by this method. We can also check our answer that whether it's equal or not at last. So, let's solve!!

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➤ Solution :-

${\sf \longrightarrow \underline{\boxed{\sf Average = \dfrac{Sum \: of \: all \: observations}{Number \: of \: observations}}}}$

Substitute the given values.

${\sf \leadsto 11 = \dfrac{8 + 9 + 12 + 16 + p}{5}}$

Add all the values on numerator in LHS.

${\sf \leadsto 11 = \dfrac{45 + p}{5}}$

Shift the number 5 from RHS to LHS, changing it's sign.

${\sf 45 + p = 11 \times 5}$

Multiply the numbers on RHS.

${\sf \leadsto 45 + p = 55}$

Shift the number 45 from LHS to RHS, changing it's sign.

${\sf \leadsto p = 55 - 45}$

Subtract the values to get the answer.

${\sf \leadsto p = 10}$

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${\red{\underline{\boxed{\bf So, \: the \: value \: of \: p \: is \: 10.}}}}$

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Verification :-

${\sf \leadsto 11 = \dfrac{8 + 9 + 12 + 16 + p}{5}}$

Substitute the value of p.

${\sf \leadsto 11 = \dfrac{8 + 9 + 12 + 16 + 10}{5}}$

Add the numbers on numerator.

${\sf \leadsto 11 = \dfrac{55}{5}}$

Simplify the fraction on RHS.

${\sf \leadsto 11 = 11}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!