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Calculate the Spearman's ranks correlation coefficient for the following data and interpret the result:

image

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xi yi Ri Ry di di2
35 40 9.5 9 0.5 0.25
54 60 8 8 0 0
80 75 5 4 1 1
95 90 1 2 -1 1
73 70 6.5 7 -0.5 0.25
73 75 6.5 4 2.5 6.25
35 38 9.5 10 -0.5 0.25
91 95 2 1 1 1
83 75 3 4 -1 1
81 71 4 6 -2 4
\(\sum d_i^2 = 15\)

spearman's rank co-relation coefficient

is \(\rho\) = 1 - \(\frac{6\sum d_i^2}{n(n^2-1)}\) = \(1-\frac{6\times15}{10\times99}\) = 1 - \(\frac1{11}\) = \(\frac{10}{11}\)

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spearman rank coefficientimageimageimage

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