Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

# The mean of five numbers is 10. I add one more number and the mean is now 11. What number did I add?

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• If the mean of five numbers is 10 it was created by adding 5 numbers together and dividing by 5.

Reverse that and multiply 10 by 5.

10 x 5 = 50....Which is the total of the 5 numbers.

To get a mean of 11 you would need to add 6 numbers together and divide by 6 to get an answer of 11.

Reverse that and multiply 11 x 6

11 x 6 = 66....which is the total of 6 numbers

the difference between the totals of 66 and 50 = 66 - 50 = 16

ANS 16

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• If the mean was 10 and there were 5 numbers

then the total of the 5 numbers added together must have been 50

because 50 divided by 5 = 10

So ..

If the mean is now 11 and there are 6 numbers

the total of the 6 numbers added together must be 66

because 66 divided by 6 = 11

and because ...

66 - 50 = 16

The number you added is 16

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• Let x be the sum of the five numbers.

x/5 = 10

x = 50

Let y be the 6th number.

(50 + y)/6 = 11

50 + y = 66

y = 16

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• --

New Total is 50 + x , mean = 11

( 50 + x ) / 6 = 11

50 + x = 66

x = 16

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• (x(1) + ...x(5)) / 5 = 10.1

(x(1) + ...x(5) + x(6)) / 6 = 11

Hence

x(1) + ...x(5) = 50.5

x(1) + ...x(5) + x(6) = 66

Subtract

x(6) = 15.5

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• 10*5=50

11*6=66

66-50=16

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• The mean of five numbers is 10.

I add one number and the mean is now 11.

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• The new number is 16 because 50+16 = 66 and 66/6 = 11

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• The mean of 5 numbers is 10.

Let's set up this expression:

s = a + b + c + d + e

The sum of the 5 numbers. So if the mean is 10, we know what this sum is:

(a + b + c + d + e) / 5 = 10

s / 5 = 10

s = 50

You add one more number (f) the mean is now 11, so:

(a + b + c + d + e + f) / 6 = 11

The sum of a through e is "s", so:

(s + f) / 6 = 11

We know the value of s:

(50 + f) / 6 = 11

Now we can solve for f:

50 + f = 66

f = 16

The new number added was 16.

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• If the mean of 5 numbers is 10, that means they all add up to 50.

50/5 = 10

In the second case, you have 6 numbers with an average of 11, so they must add up to 66:

66/6 = 11

In order to go from 50 to 66, you must have added 16.

66 - 50 = 16

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