Multiple choice

If the mean of following frequency. distribution. is $2.6$, then the value of $f$ is $x_i$ 1 2 3 4 5 $f_i$ 5 4 f 2 3

  1. $1$
  2. $3$
  3. $8$
  4. none of these

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A Correct answer
Explanation

Mean = sum(f*x) / sum(f). Sum(f*x) = 1*5 + 2*4 + 3*f + 4*2 + 5*3 = 5 + 8 + 3f + 8 + 15 = 36 + 3f. Sum(f) = 5 + 4 + f + 2 + 3 = 14 + f. Setting (36 + 3f) / (14 + f) = 2.6: 36 + 3f = 36.4 + 2.6f, so 0.4f = 0.4, f = 1.