Question

The mean of 5 numbers is 27 if one number is excluded their mean is 25 find the excluded number

Answer 1

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

The Excluded number is 47

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

Given :

Mean of 5 numbers = 27

One number excluded the new mean = 25

To Find :

The Excluded number

Solution :

$\textbf{Case I}$

Here,

• Mean = 27
• Observations = 5
• Sum of Observations = x

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

$\sf{\implies} \: 27 = \dfrac{x}{5}$

$\sf{\implies} \: 27 \times 5 = x$

$\sf{\implies} \: x = 135$

Sum of Observations in Case I is 135

$\rule{300}{1.5}$

$\textbf{Case II}$

Here,

• Mean = 22
• Observations = 4 (one number Excluded)
• Consider Excluded number as y
• Sum of Observations = 135 - y

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

$\sf{\implies} \:22 = \dfrac{135 - y}{4}$

$\sf{\implies} \:22 \times 4 = 135 - y$

$\sf{\implies} \:88 = 135 - y$

$\sf{\implies} \:y= 135 - 88$

$\sf{\implies} \:y = 47$

$\therefore$ The Excluded number is 47.