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Write down the given ages and the mean.

Mathematics

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Answer

5\text{5}

Step-by-step solution

5 steps
  1. Write down the given ages and the mean.

    The ages are 8,11,8,10,5,7,2u,11,118, 11, 8, 10, 5, 7, 2u, 11, 11.
    The number of ages is n=9n=9.
    The mean age is 9 years.

  2. Use the formula for the mean.

    The mean is the sum of all values divided by the number of values.

    Mean=∑agesn\text{Mean} = \frac{\sum \text{ages}}{n}
  3. Substitute the given values into the mean formula.

    9=8+11+8+10+5+7+2u+11+1199 = \frac{8 + 11 + 8 + 10 + 5 + 7 + 2u + 11 + 11}{9}
  4. Sum the known numerical values in the numerator.

    8+11+8+10+5+7+11+11=718 + 11 + 8 + 10 + 5 + 7 + 11 + 11 = 71

    So the equation becomes:

    9=71+2u99 = \frac{71 + 2u}{9}
  5. Solve for uu.

    Multiply both sides by 9:

    9×9=71+2u9 \times 9 = 71 + 2u 81=71+2u81 = 71 + 2u

    Subtract 71 from both sides:

    81−71=2u81 - 71 = 2u 10=2u10 = 2u

    Divide by 2:

    u=102u = \frac{10}{2} u=5u = 5

    The value of uu is 5\boxed{\text{5}}.

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