Multiple choice

The frequency of numbers 3, 5, 6, 4 is respectively x, x + 2, x - 8 and x. If their mean is 4, then value of x will be ________.

  1. 3

  2. 6

  3. 7

  4. 8
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C Correct answer
Explanation

The mean is calculated as the sum of (value * frequency) divided by the total frequency. Sum = 3x + 5(x+2) + 6(x-8) + 4x = 18x - 38. Total frequency = x + x+2 + x-8 + x = 4x - 6. Setting (18x-38)/(4x-6) = 4, we get 18x - 38 = 16x - 24, which simplifies to 2x = 14, so x = 7.

AI explanation

The formula for the mean of a frequency distribution is the sum of each value multiplied by its frequency, divided by the total frequency. The numerator is 3x + 5(x + 2) + 6(x - 8) + 4x, which simplifies to 18x minus 38. The denominator is x + (x + 2) + (x - 8) + x, which simplifies to 4x minus 6. Setting the mean to 4 gives the equation (18x - 38) / (4x - 6) = 4. Cross-multiplying yields 18x - 38 = 16x - 24, so 2x = 14 and x = 7. The result is 7.

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