Question

15) If the mean of 4, 7, x, 13 and 16 is 10. find x​

Answer 1

Answer:

mean =sum of observations/ total observation

10 = 4+7+x+13+16/ 5

10*5 = 40+x

50 - 40 = x

x = 10

             

Answer 2

★ How to do :-

Here, we are given with a data that has five observations. We are also given with the mean value of the data. But, we aren't given with one of the observation which we are asked to find the same. The observation that is not provided is replaced by a variable x. We are asked to find the value of the same variable x. Here, we use the concept of finding the mean of observation. Mean of the data can also be said as the average or arithrmetic mean. We can also check our answer by verification method which will be done at last. So, let's solve!!

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➤ Solution :-

Mean :-

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

Substitute the given values.

${\tt \leadsto 10 = \dfrac{4 + 7 + x + 13 + 16}{5}}$

Add all the values on numerator of RHS.

${\tt \leadsto 10 = \dfrac{x + 40}{5}}$

Shift the number 50 from LHS to RHS.

${\tt \leadsto 10 \times 5 = x + 40}$

Multiply the values on LHS.

${\tt \leadsto 50 = x + 40}$

Shift the number 40 from RHS to LHS, changing it's sign.

${\tt \leadsto x = 50 - 40}$

Subtract the values to get the value of x.

${\tt \leadsto x = 10}$

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

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Verification :-

${\tt \leadsto 10 = \dfrac{4 + 7 + x + 13 + 16}{5}}$

Substitute the value of x.

${\tt \leadsto 10 = \dfrac{4 + 7 + 10 + 13 + 16}{5}}$

Add all the values on numerator.

${\tt \leadsto 10 = \dfrac{50}{5}}$

Simplify the fraction on RHS.

${\tt \leadsto 10 = 10}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!