Multiple choice

If mean of the following frequency distribution is $1.46$ then find the unknown frequency. x: 0 1 2 3 4 5 Total f: 46 ... ... 25 10 5 200

  1. $38$ and $76$
  2. $35$ and $72$
  3. $38$ and $71$
  4. $32$ and $72$
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A Correct answer
Explanation

The sum of the frequencies is 200, which gives the equation f1 + f2 = 114. Using the formula for the mean, we get another equation f1 + 2*f2 = 152. Solving this system of linear equations yields f1 = 76 and f2 = 38.

AI explanation

Let the unknown frequencies be f1 and f2. Based on the total frequency of 200, we establish the equation f1 plus f2 plus 46 plus 25 plus 10 plus 5 equals 200, which simplifies to f1 plus f2 equals 114. Using the given mean of 1.46, we set up the equation for the sum of observations divided by total frequency: 0 multiplied by f1 plus 1 multiplied by f1 plus 2 multiplied by f2 plus 75 plus 40 plus 25 equals 1.46 multiplied by 200, simplifying to f1 plus 2f2 plus 140 equals 292, or f1 plus 2f2 equals 152. Solving the system of equations yields f1 equals 76 and f2 equals 38.

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