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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  • RR
    Lv 7
    6 months ago

    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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  • geezer
    Lv 7
    6 months ago

    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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  • 6 months ago

    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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  • Como
    Lv 7
    6 months ago

    --

    New Total is 50 + x , mean = 11

    ( 50 + x ) / 6 = 11

    50 + x = 66

    x = 16

    Number added is 16

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  • 6 months ago

    (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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  • 6 months ago

    10*5=50

    11*6=66

    66-50=16

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  • 6 months ago

    The mean of five numbers is 10.

    I add one number and the mean is now 11.

    What number did I add?

    You added the number 16.

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  • David
    Lv 7
    6 months ago

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

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  • 6 months ago

    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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  • 6 months ago

    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

    Answer:

    16

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