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  • 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 : (A) 46.5 (B) 49.5 (C) 53.5 (D) 56.5

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 :

(A) 46.5

(B) 49.5

(C) 53.5

(D) 56.5

Answers (1)

Answer : D

Given that there are 50 numbers.

Let the numbers be

x,y,z.........\left ( 50\; nos. \right )

\text {Mean is defined as }=\frac{\text {sum of observations}}{\text {Number of observations}}

\text {Original mean }=\frac{(x+y+z+......)}{50}

Each number is subtracted from 53

New numbers =53-x,53-y,53-z......

Sum of new numbers =53-x+53-y+53-z+......

The new mean is given as -3.5

-3.5=\frac{53-x+53-y+53-z+.....}{50}

-3.5=\frac{\left ( 53 \right )\left ( 50 \right )-\left ( x+y+z+..... \right )}{50}

-3.5=\frac{(53)(50)}{50}-\frac{\left ( x+y+z+.... \right )}{50}

-3.5=53-\text {original mean}

Original mean =53+3.5=56.5

Therefore option (D) is correct.

 

Posted by

infoexpert23

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