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29 September, 02:10

The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number.

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  1. 29 September, 02:25
    0
    Answer: The thirteenth number is 29

    Step-by-step explanation: We shall by looking at the available bits of information. We already have a mean of 12 positive numbers which is 3. The addition of the numbers divided by 12 would result in the mean. This we can express as follows;

    Summation/12 = 3

    That basically is the formula for calculating a set of data/numbers.

    If we cross multiply, the expression becomes;

    Summation = 3 x 12

    Summation = 36.

    That means if we add up all 12 positive numbers we would have 36. When another is added the mean becomes 5. That is,

    (36 + a) / 13 = 5

    That means the summation is now 36 + a, and the observed data is now 13, while the mean is now 5. Therefore,

    (36 + a) / 13 = 5

    We cross multiply and we have,

    36 + a = 5 x 13

    36 + a = 65

    Subtract 36 from both sides of the equation

    a = 29

    Therefore the 13th number is 29.
  2. 29 September, 02:29
    0
    29

    Step-by-step explanation:

    Let a12 be the mean of the first 12 numbers:

    a12 = (sumOf12Numbers) / 12.

    So, sumOf12Numbers=12*a12

    We add a new number, x:

    a13 = (sumOf12Numbers+x) / 13

    13*a13=12*a12+x

    x=13*a13-12*a12=13*5-12*3=65-36=29

    The thirteenth number is 29
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