Question

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5. The mean of the given numbers is :​

Answer 1

Answer:

56.5

Step-by-step explanation:

Total numbers =50

Mean of numbers after subtracting 53 from each =3.5

Sum of numbers after subtracting 53 from each =3.5×50=175

Sum of the original numbers =175+53×50=2825

Mean of the original numbers =502825=56.5

HOPE IT HELPS..

Answer 2

Step-by-step explanation:

Given that n=50 , then

$\pmb{\color{darkcyan} \[ \begin{aligned} \operatorname{Mean}(\bar{x}) & \tt=\frac{\sum_{i=1}^{n} x_{i}}{n} \\ \\ & \tt=\frac{1}{50} \times \sum_{i=1}^{50} x_{i} \qquad\qquad\ldots(i)\\ \\ \tt \Rightarrow \sum_{i=1}^{50} x_{i} &=50 \bar{x} \end{aligned} \]}$

Now, subtract each observation from 53 , we get a new mean, say $\tt\bar{x}_{A}$

$\color{purple} \pmb{\[ \begin{array}{l} \tt \therefore \quad \bar{x}_{A}=\dfrac{\left(53-x_{1}\right)+\left(53-x_{2}\right)+\ldots+\left(53-x_{50}\right)}{50} \\ \\ \tt \Rightarrow-3.5=\dfrac{(53+53+\ldots \text { upto } 50 \text { times })-\left(x_{1}+x_{2}+\ldots+x_{50})\right.}{50} \\ \\ \tt \Rightarrow-3.5 \times 50=53 \times 50-\left(x_{1}+x_{2}+\ldots .+x_{50}\right) \\ \\ \tt \Rightarrow \sum_{i=1}^{50} x_{i}=2650+175=2825\red{ \qquad\qquad\ldots(ii)} \\ \\ \tt \therefore \text { Mean of } 50 \text { observations }=\dfrac{1}{50} \times 2825=56.5 \\ \\ \tt {[\text { From (i) and (ii) }]} \end{array} \]}$