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I know

  • the average of a group that consists of two subgroups.
  • the number in the two subgroups
  • the total
  • the average of one of the subgroups.

How can I work out the average of the other subgroup?

Basically, overall average of group of say 200 is 65%, subgroup B which is 150 has an average of 70%, subgroup C is 50. What is the average score of subgroup C?

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1 Answer 1

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$m_1$ - known average in the first subgroup
$m_2$ - unknown average in the second subgroup
$m$ - known total average
$n_1$ - number of points in the first subgroup
$n_2$ - number of points in the second subgroup
$n$ - number of points in total

You have $$n \cdot m = m_1 \cdot n_1 + m_2 \cdot n_2$$ So... $$m_2 = \frac{n \cdot m - m_1 \cdot n_1}{n_2}$$

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