Question

There are $50$ numbers. If each number is subtracted from $53$, then the mean of the numbers so obtained is $-3.5$. Find the mean of the given numbers.

Answer 1

$\begin{array}{c}{x}_1,x_2,x_3,......x_{50}\\ x_1-53,x_2-53,x_3-53,.........\left(asperquestion\right)\\ Asperquestion\\ x_1+x_2+x_3\\ Meansof50number\left(asperquestion\right)\\ y_1=\frac{x_1+x_2+x_3+......x_{50}}{50}=........\left(i\right)\\ let{y}_{2}willbemeanof\\ y_2=\frac{x_1-53+x_2-\mathrm{53......}{x}_{50}-53.}{50}\left(\therefore y_2=-3.5given\right)\\ -3.5=\frac{x_1+x_2+x_3}{50}........\frac{50\times 53}{50}\\ -3.5=y_1-53\\ y=53-3.5\\ y=49.5\end{array}$