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Nov 2007 p6 q1
2536
A summary of 24 observations of \(x\) gave the following information:
\(\Sigma(x-a) = -73.2\) and \(\Sigma(x-a)^2 = 2115\).
The mean of these values of \(x\) is 8.95.
Find the value of the constant \(a\).
Find the standard deviation of these values of \(x\).
Solution
(i) We know that \(\Sigma(x-a) = -73.2\). Since there are 24 observations, the mean of \(x-a\) is \(\frac{-73.2}{24} = -3.05\). Given that the mean of \(x\) is 8.95, we have:
\(a = 8.95 + 3.05 = 12\)
(ii) The standard deviation is calculated using:
\(\text{Standard deviation} = \sqrt{\frac{\Sigma(x-a)^2}{24} - (\text{mean of } x-a)^2}\)