Question

The mean of 5 number is 30 if one number is excluded their mean become 28 what is the excluded number

Answer 1

Answer:

no. is 38

Step-by-step explanation:

mean= sum/total no. of observation

30=sum/5

sum= 150

new mean = sum/total no. of observation

28=sum/4

sum= 112

excluded number=150-112

=38

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Excluded number is 38.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Mean of 5 numbers = 30

If one Number is excluded new mean = 28

To find :

The Excluded number

Solution :

$\textbf{Case I}$

Here,

Mean = 30

Observations = 5

Consider Sum of Observations as x

★ $\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\implies} \: 30 = \dfrac{x}{5}$

$\sf{\implies} \:x = 30 \times 5$

$\sf{\implies} \:x = 150$

Sum of the observations when the number is included is 150

$\rule{300}{1.5}$

$\textbf{Case II }$

Here,

Mean = 28

Observations = 4 (One Number is Excluded)

Consider the number excluded as y

Sum of Observations = 150 - y

★ $\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\implies} \:28 = \dfrac{150 - y}{4}$

$\sf{\implies} \:112 = 150 - y$

$\sf{\implies} \:y = 150 - 112$

$\sf{\implies} \:y = 38$

$\therefore$ The Excluded number is 38.