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Combining the means of two classes

Combining the means of two classes

IP 1
6 marks

Class A has \(20\) students with mean mark \(64\). Class B has \(25\) students with mean mark \(70\).

  1. Find the mean mark of all \(45\) students.[2]
  2. Ali says the combined mean is \(\dfrac{64+70}{2}=67\). Explain why he is wrong, and state when his method would give the correct answer.[2]
  3. A mark in class A was recorded as \(46\) instead of \(64\). Find the corrected mean of all \(45\) students.[2]

Solution:

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Answer:(a) \(67\dfrac13\) (b) the classes have different sizes; it works only for equal-sized classes (c) \(67\dfrac{11}{15}\)

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