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 number isa)47.5b)52.5c)56.5d)49.5Correct answer is option 'C'. Can you explain this answer?

Question

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be &ndash; 3.5. The mean of the given number isa)47.5b)52.5c)56.5d)49.5Correct answer is option 'C'. Can you explain this answer?

Answer

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 =2825/50=56.5

Answer

Let x be the mean of 50 numbers.

∴ sum of 50 numbers = 50x

Since each number is subtracted from 53.

According to question, we have

53 × 50 - 50x / 50 = - 3.5

⇒ 2650 - 50x = -175 ⇒ 50x = 2825

⇒ x = 2825 / 50 = 56.5

Answer

29. What is the mean of the original 50 numbers?

Let's call the original 50 numbers x1, x2, x3,...,x50.

We know that when each number is subtracted from 53, the resulting numbers have a mean of 29. This means that:

(53 - x1) + (53 - x2) + (53 - x3) + ... + (53 - x50)

has a mean of 29. We can simplify this expression by distributing the 53's and factoring out a -1:

(53 + 53 + 53 + ... + 53) - (x1 + x2 + x3 + ... + x50)

has a mean of 29. The first part simplifies to:

53 x 50 = 2650

So we have:

2650 - (x1 + x2 + x3 + ... + x50)

has a mean of 29.

We can now use the formula for the mean of a set of numbers:

mean = (sum of numbers) / (number of numbers)

to find the sum of the x's. We know that there are 50 x's, and we can rearrange the equation above to get:

sum of x's = 2650 - 29 x 50 = 1350

Now we can find the mean of the x's using the formula:

mean = (sum of numbers) / (number of numbers)

mean = 1350 / 50 = 27

So the mean of the original 50 numbers is 27.

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