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In a test, the mean score of the girls in a class is 60 and their variance is 20 . The mean score of the boys is 80 . If the overall mean score of the class is 68 and the overall variance is 120 , then the variance of the boys' scores is

Options

  1. A270
  2. B30
  3. C0
  4. D246

Correct answer

B. 30

Step-by-step solution

Let the number of girls be n_g and the number of boys be n_b . The combined mean is given by: _c = n_g _g + n_b _b n_g + n_b Substituting the given values: 68 = 60n_g + 80n_b n_g + n_b 68n_g + 68n_b = 60n_g + 80n_b 8n_g = 12n_b n_g n_b = 3 2 Let n_g = 3k and n_b = 2k . The deviations of the individual means from the combined mean are: d_g = _g - _c = 60 - 68 = -8 d_b = _b - _c = 80 - 68 = 12 The formula for combined variance is: _c^2 = n_g( _g^2 + d_g^2) + n_b( _b^2 + d_b^2) n_g + n_b Substituting the known values:

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