Multiple choice

The mean of the following distribution is $4$. Find the value of $q$. $x$ $2$ $3$ $4$ $5$ $7$ $f$ $4$ $4$ $2$ $3$ $q$

  1. $2$
  2. $3$
  3. $0$
  4. $4$
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B Correct answer
Explanation

The mean is calculated as sum(x*f) / sum(f). Setting up the equation (2*4 + 3*4 + 4*2 + 5*3 + 7*q) / (4+4+2+3+q) = 4 simplifies to (8 + 12 + 8 + 15 + 7q) / (13 + q) = 4. Solving 43 + 7q = 52 + 4q leads to 3q = 9, so q = 3.

AI explanation

Using the direct method for the arithmetic mean, the sum of the observations is 8 + 12 + 8 + 15 + 7q = 43 + 7q, and the total frequency is 4 + 4 + 2 + 3 + q = 13 + q. Setting the mean equal to 4 gives the equation (43 + 7q) / (13 + q) = 4, which simplifies to 43 + 7q = 52 + 4q. Solving 3q = 9 yields q = 3.

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