Multiple choice

The frequencies of numbers 3, 5, 7 and 9 respectively are x - 2, x + 2, x - 3 and x + 3 and their arithmetic mean is 6.5. Find the value of x.

  1. 3

  2. 5

  3. 4

  4. 6
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B Correct answer
Explanation

Mean = sum(f*x) / sum(f). Sum of frequencies = (x-2)+(x+2)+(x-3)+(x+3) = 4x. Sum of (f*x) = 3(x-2) + 5(x+2) + 7(x-3) + 9(x+3) = 3x-6 + 5x+10 + 7x-21 + 9x+27 = 24x + 10. Mean = (24x+10)/4x = 6.5. 24x+10 = 26x, so 2x = 10, x = 5.

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