Multiple choice

The mean of following distribution is $6.5$. Find the value of $k$. $x$ $2$ $4$ $6$ $8$ $10$ $f$ $5$ $3$ $7$ $6$ $k$

  1. $5$
  2. $4$
  3. $7$
  4. $8$
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C Correct answer
Explanation

Mean = sum(f*x) / sum(f). 6.5 = (2*5 + 4*3 + 6*7 + 8*6 + 10*k) / (5+3+7+6+k). 6.5 = (10+12+42+48+10k) / (21+k). 6.5(21+k) = 112 + 10k. 136.5 + 6.5k = 112 + 10k. 24.5 = 3.5k. k = 7.

AI explanation

Using the arithmetic mean formula, the sum of the products is 10 + 12 + 42 + 48 + 10k = 112 + 10k, and the total frequency is 5 + 3 + 7 + 6 + k = 21 + k. Setting the mean equal to 6.5 gives the equation (112 + 10k) / (21 + k) = 6.5, which simplifies to 112 + 10k = 136.5 + 6.5k. Solving 3.5k = 24.5 yields k = 7.

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