Question

the arithmetic mean of 80 numbers is 55 . if two numbers namely 250 and 850 are removed what is the arthmatic mean of remaing number​

Answer 1

Answer:

$\sf{The \ arithmetic \ mean \ of \ remaining} \\ \sf{numbers \ is \ 42.31}$

Given:

$\sf{The \ arithmetic \ mean \ of \ 80 \ numbers \ is 55 .}$

To find:

$\sf{If \ two \ numbers \ 250 \ and \ 850 \ are}$

$\sf{removed. \ What \ is \ the \ arithmetic \ mean}$

$\sf{of \ remaining \ numbers.}$

Solution:

$\sf{Arithmetic \ mean=\dfrac{Sum \ of \ observations}{Number \ of \ observations}} \\ \\ \sf{\therefore {55=\dfrac{Sum \ of \ 80 \ observations}{80}}} \\ \\ \sf{\therefore{Sum \ of \ 80 \ observations=55\times80}} \\ \\ \sf{\therefore{Sum \ of \ 80 \ observations=4400}} \\ \\ \sf{Two \ observations \ 250 and \ 850 \ are \ removed} \\ \\ \sf{\therefore{Now, \ number \ of \ observations=80-2=78}} \\ \\ \sf{Sum \ of \ 78 \ observations=Sum \ of \ 80 \ observations-(250+850)} \\ \\ \sf{\therefore{Sum \ of \ 78 \ observations=4400-1100}} \\ \\ \sf{Sum \ of \ 78 \ observations=3300} \\ \\ \sf{Now, \ arithmetic \ mean \ of \ remaining \ 78 \ numbers} \\ \\ \sf{Arithmetic \ mean=\dfrac{Sum \ of \ 78 \ observations}{78}} \\ \\ \sf{\therefore{Arithmetic \ mean=\dfrac{3300}{78}}} \\ \\ \sf{\therefore{Arithmetic \ mean = 42.31(approx)}} \\ \\ \sf\purple{\tt{\therefore{The \ arithmetic\ mean \ of}}} \\ \sf\purple{\tt{remaining \ numbers \ is \ 42.31}}$