Multiple choice

Consider the frequency distribution of the given number Value 1 2 3 4 frequency 5 4 0 f If mean of the distribution is equal to 3, then the value of ' f ' is

  1. $7$
  2. $9$
  3. $12$
  4. $14$
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D Correct answer
Explanation

Mean = (1*5 + 2*4 + 3*0 + 4*f) / (5+4+0+f) = 3. (5 + 8 + 4f) / (9+f) = 3. 13 + 4f = 27 + 3f. f = 14.

AI explanation

The formula for the mean of a frequency distribution is the sum of each value times its frequency divided by the total frequency. Setting up the equation yields 3 = (5 + 8 + 0 + 4f) / (5 + 4 + 0 + f), which simplifies to 3 = (13 + 4f) / (9 + f). Multiplying both sides by (9 + f) gives 27 + 3f = 13 + 4f. Solving this equation results in f = 14.

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