Question

19. 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

Answer 1

Answer:

B 49.5

Step-by-step explanation:

let the mean be m

the numbers be x1 x2 x3 x4 x50

$m = \frac{x1 + x2 + ... + x50}{50} \\ \\ given \\ \\ - 3.5 = \frac{(x1 - 53) + (x2 - 53) + ..... + (x50 - 53)}{50} \\ \\ - 3.5 = \frac{x1 + x2 + ... + x50}{50} - \frac{53(50)}{50} \\ \\ \frac{x1 + x2 + ... + x50}{50} = 49.5 \\ \\ m = 49.5$

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Answer 2

Answer:

B 49.5

Step-by-step explanation:

let the mean be m

the numbers be x1 x2 x3 x4 x50

$\begin{lgathered}m = \frac{x1 + x2 + ... + x50}{50} \\ \\ given \\ \\ - 3.5 = \frac{(x1 - 53) + (x2 - 53) + ..... + (x50 - 53)}{50} \\ \\ - 3.5 = \frac{x1 + x2 + ... + x50}{50} - \frac{53(50)}{50} \\ \\ \frac{x1 + x2 + ... + x50}{50} = 49.5 \\ \\ m = 49.5 \\ \\\end{lgathered}$