Combined with coded data

Questions where at least one group's data is given in coded form like Σ(x-a) and Σ(x-a)², requiring decoding before combining groups.

1 questions · Standard +0.3

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CAIE S1 2024 June Q1
4 marks Standard +0.3
1 A summary of 20 values of \(x\) gives $$\Sigma ( x - 30 ) = 439 , \quad \Sigma ( x - 30 ) ^ { 2 } = 12405 .$$ A summary of another 25 values of \(x\) gives $$\sum ( x - 30 ) = 470 , \quad \sum ( x - 30 ) ^ { 2 } = 11346 .$$
  1. Find the mean of all 45 values of \(x\).
  2. Find the standard deviation of all 45 values of \(x\).