Feb/Mar 2016 p62 q1
2517
For 10 values of x the mean is 86.2 and \(\Sigma(x-a) = 362\). Find the value of
- \(\Sigma x\),
- the constant a.
Solution
Given that the mean of 10 values is 86.2, we have:
\(\frac{\Sigma x}{10} = 86.2\)
Therefore, \(\Sigma x = 86.2 \times 10 = 862\).
For part (ii), we know \(\Sigma(x-a) = 362\).
Expanding this, we have:
\(\Sigma x - 10a = 362\)
Substituting \(\Sigma x = 862\) from part (i):
\(862 - 10a = 362\)
Solving for \(a\):
\(10a = 862 - 362\)
\(10a = 500\)
\(a = 50\)
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