Given that \(n = 10\) and \(\sum d^{2} = 20\), calculate the Spearman's rank correlation coefficient.
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Correct Answer: Option C
Explanation:
The Spearman's correlation coefficient \(\rho\) is given as:
\(\rho = 1 - \frac{6\sum d^{2}}{n(n^{2} - 1)}\)
= \(\rho = 1 - \frac{6 \times 20}{10(10^{2} - 1)}\)
= \(1 - \frac{120}{990} = \frac{870}{990}\)
= \(0.879\)
The Spearman's correlation coefficient \(\rho\) is given as:
\(\rho = 1 - \frac{6\sum d^{2}}{n(n^{2} - 1)}\)
= \(\rho = 1 - \frac{6 \times 20}{10(10^{2} - 1)}\)
= \(1 - \frac{120}{990} = \frac{870}{990}\)
= \(0.879\)