Question

if the mean of 25 observations is 27 and each observations is decreased by 7,what will be the new mean.please solve it in copy.its urgent please please solve it fast please please

Answer 1

$\textsf{We know that :}$

✿  $\boxed{\sf{Mean = \dfrac{Sum\;of\;all\;Observations}{Total\;Number\;of\;Observations}}}$

$\textsf{Given : The Total Number of Observations = 25}$

$\sf{Let\;the\;Observations\;be\;denoted\;by: O_1,\;O_2,\;O_3.\;.\;.\;.\;O_2_5}$

$\textsf{Given : The Mean of 25 Observations is 27}$

$\sf{\implies \dfrac{O_1 + O_2 + O_3\;.\;.\;.\;+\;O_2_5}{25} = 27}$

$\sf{\implies O_1 + O_2 + O_3\;.\;.\;.\;+\;O_2_5 = 27 \times 25}$

$\sf{\implies O_1 + O_2 + O_3\;.\;.\;.\;+\;O_2_5 = 675 }$

$\textsf{Given : Each Observation is decreased by 7}$

$\sf{\implies New\;Mean = \dfrac{(O_1 - 7) + (O_2 - 7) + (O_3 - 7)\;.\;.\;.\;+\;(O_2_5 - 7)}{25}}\\\\\\\sf{\implies New\;Mean = \dfrac{(O_1 + O_2 + O_3\;.\;.\;.\;+\;O_2_5) - (25 \times 7)}{25}}\\\\\\\sf{\implies New\;Mean = \dfrac{675 - 175}{25}}\\\\\\\sf{\implies New\;Mean = \dfrac{500}{25}}\\\\\\\sf{\implies New\;Mean = 20}$