Question

mean of 5 numbers is 22, if one the is excluded the mean reduces by 2 what is the excluded no?

Answer 1

$\huge\mathsf{\underline{ \ Given \ : \ }}$


$\mathsf\red{\implies \ Mean \ = \ 22}$



$\mathsf\red{\implies \ Total \ numbers \ = \ 5}$



$\huge\mathsf{\underline{ \ Solution \ : \ }}$



${\boxed{\mathsf{\blue{Mean \ = \ {\dfrac{Sum \ of \ all \ numbers}{Total \ numbers}}}}}}$



$\mathsf\blue{Putting \ values}$



$\mathsf\blue{\implies \ 22 \ = \ {\dfrac{Sum \ of \ 5 \ numbers}{5}}}$



$\mathsf\blue{\implies \ Sum \ of \ 5 \ numbers \ = \ 110}$



$\mathsf\blue{We \ can \ also \ write \ this \ -}$



$\mathsf\blue{\implies \ Sum \ of \ 4 \ numbers \ + \ Excluded}$
$\mathsf\blue{number \ = \ 110}$



$\mathsf\blue{Let, \ excluded \ number \ = \ x}$



$\blue\therefore$



$\mathsf\blue{\implies \ Sum \ of \ 4 \ numbers \ + \ x \ = \ 110}$
$\mathsf\blue{ \qquad \qquad \qquad \qquad \qquad \qquad \qquad ....( \ 1 \ )}$



$\mathsf\blue{A/q}$



$\mathsf\blue{If \ x \ is \ excluded, \ then \ -}$



$\mathsf\blue{\implies \ New \ Mean \ = \ 22 - 2 \ = \ 20}$



$\mathsf\blue{\implies \ Total \ numbers \ = \ 4}$



$\mathsf\blue{\implies \ New \ Mean \ = \ {\dfrac{Sum \ of \ 4 \ numbers}{Total \ numbers}}}$



$\mathsf\blue{Putting \ values}$



$\mathsf\blue{\implies \ 20 \ = \ {\dfrac{Sum \ of \ 4 \ numbers}{4}}}$



$\mathsf\blue{\implies \ Sum \ of \ 4 \ numbers \ = \ 80}$



$\mathsf\blue{Putting \ this \ in \ ( \ 1 \ ), \ we \ get}$



$\mathsf\blue{\implies \ 80 \ + \ x \ = \ 110}$



$\mathsf\blue{\implies \ x \ = \ 110 - 80}$



$\mathsf\blue{\implies \ x \ = \ 30}$



${\boxed{\boxed{\mathsf{\blue{\implies \ Excluded \ number \ = \ 30}}}}}$