Question

The mean of 40, 52 , 74, X , 36 is 46. Find the value of the observation x.
30
38
20
28​

Answer 1

Mean of 40, 52 , 74, x , 36 = 46

We have to find out the value of x.

Now, we know that :-

$\underline{\boxed{ \boxed{ \tt \large mean \: of \: given \: observations = \dfrac{sum \: of \: observations}{total \: number \: of \: observations} }}}$

$\tt \rightarrow sum \: of \: given \: observations = 40 + 52 + 74 + x + 36 \\ \\ \tt \rightarrow40 + 52 + 74 +x + 36 = 202 + x$

$\tt \rightarrow total \: number \: of \: given \: observations = 5$

$\tt \longrightarrow 46= \dfrac{202 + x}{5}$

$\tt \longrightarrow 46 \times 5= {202 + x}$

$\tt \longrightarrow 230= {202 + x} \\ \\ \tt \longrightarrow 230 - 202= { x}\tt \\ \\ \tt \longrightarrow 28= {x}$

Answer :

Value of x = 28

Therefore, last option is correct.

$\tt \large \red{Verification\: of \:answer :}$

We will find mean of 40, 52 , 74, 28 , 36 . If we get mean as 46 then our answer x = 28 is correct.

$\tt \rightarrow mean \: of \: given \: observations = \dfrac{sum \: of \: observations}{total \: number \: of \: observations}$

$\tt \rightarrow \dfrac{40 + 52 + 74 + 28 + 36}{5} = \dfrac{230}{5}$

$\tt \rightarrow \dfrac{230}{5} = 46$

Hence verified

Therefore, our answer x = 28 is correct.

Answer 2

Mean of 40, 52 , 74, x , 36 = 46

We have to find out the value of x.

Now, we know that :-

Mean of observations = sum of observations/ Total number of observations

sum of given observations = 40 + 52 + 74 + x + 36

= 40 + 52 + 74 + x + 36 = 202 + x

Total number of observations = 5

= 46 = 202 + x / 5

= 45 × 5 = 202 + x

= 230 = 202 + x

= 230 - 202 = x

= 28 = x

Hence verified

Therefore, our answer x = 28 is correct.