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  • What is the mean of 20 numbers that are obtained by subtracting each number from 25, if the resulting mean of these numbers is 2.5?    <div cla

What is the mean of 20 numbers that are obtained by subtracting each number from 25, if the resulting mean of these numbers is 2.5?

 

 

Option: 1

27.5


Option: 2

29.5


Option: 3

23.5

 


Option: 4

26.5


Answers (1)

best_answer

option (A) 27.5

Let's assume that the mean of the original 20 numbers is x. 

Let the numbers be \mathrm{ x_{1}, x_{2},..., x_{20}}

Therefore, we get,

             \mathrm{ x=\frac{x_{1}+x_{2}+...+x_{20}}{20}}

We know that each number is subtracted from 25 to obtain a new set of 20 numbers. 

So, the new observations after subtracting 25 from each number is, 

 \mathrm{ (x_{1}-\ 25), (x_{2}-\ 25),..., (x_{20}-\ 25)}

We know the general formula for mean is,

\mathrm{\text{Mean}=\frac{\text{Sum of all observations}}{\text{Number of observations}}}

Thus, the new mean is, 

\mathrm{\text{New Mean}=\frac{(x_{1}-\ 25)+(x_{2}-\ 25)+...+(x_{20}-\ 25)}{20}}

\mathrm{\Rightarrow \text{New Mean}=\frac{x_{1}+x_{2}+...+x_{20}-\ (20\times 25)}{20}}

Put 2.5 for new mean in the above equation, therefore we have,

\mathrm{ \frac{x_{1}+x_{2}+...+x_{20}-\ (20\times 25)}{20}=2.5 }

\mathrm{\Rightarrow \frac{x_{1}+x_{2}+...+x_{20}}{20}-\frac{(20\times 25)}{20}=2.5}

\mathrm{ \Rightarrow \frac{x_{1}+x_{2}+...+x_{20}}{20}-\ 25=2.5}

\mathrm{ \Rightarrow \frac{x_{1}+x_{2}+...+x_{20}}{20}=27.5}

                               \mathrm{ \Rightarrow x=27.5}

So, the mean of the 20 numbers is 27.5.


 

Posted by

Anam Khan

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