Question Number 171499 by MathsFan last updated on 16/Jun/22
$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sample}}\:\boldsymbol{\mathrm{of}}\:\mathrm{20}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{is}} \\ $$$$\mathrm{320}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{squares}}\: \\ $$$$\:\boldsymbol{\mathrm{is}}\:\mathrm{5840}.\:\boldsymbol{\mathrm{Calculate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{mean}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{nineteen}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\mathrm{20}^{\boldsymbol{\mathrm{th}}} \: \\ $$$$\boldsymbol{\mathrm{observation}}\:\boldsymbol{\mathrm{is}}\:\mathrm{25}. \\ $$
Answered by Rasheed.Sindhi last updated on 16/Jun/22
$${Sum}\:{of}\:\mathrm{20}\:{numbers}=\mathrm{320} \\ $$$$\underset{−} {\mathrm{20}{th}\:{number}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{25}} \\ $$$${Sum}\:{of}\:{remaining}\:\mathrm{19}\:{numbers} \\ $$$$=\mathrm{320}−\mathrm{25}=\mathrm{295} \\ $$$${Mean}\:{of}\:\mathrm{19}\:{numbers}=\frac{\mathrm{295}}{\mathrm{19}}=\mathrm{15}\frac{\mathrm{10}}{\mathrm{19}} \\ $$$$ \\ $$
Commented by MathsFan last updated on 16/Jun/22
$${thank}\:{you}\:{very}\:{much}\:{sir} \\ $$