Multiple choice

Find the missing value of P for the following distribution whose mean is $12.58$ $x_i$ 5 8 10 12 P 20 25 $f_i$ 2 5 8 22 7 4 2

  1. $12$
  2. $15$
  3. $14$
  4. $16$
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B Correct answer
AI explanation

Using the direct method for arithmetic mean, the mean is calculated by dividing the sum of the products of frequency and observation by the total frequency. The total frequency is 2 plus 5 plus 8 plus 22 plus 7 plus 4 plus 2, which equals 50. The sum of the products is 10 plus 40 plus 80 plus 264 plus 7 times P plus 80 plus 50, simplifying to 524 plus 7 times P. Setting the equation equal to the mean of 12.58, we have 524 plus 7 times P divided by 50 equals 12.58, which gives 524 plus 7 times P equals 629; solving for P results in 15.

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