So r_s = 1 - \(\frac { 6\sum { { d }^{ 2 } } }{ n({ n }^{ 2 }-1) } \)= 1 - \(\frac { 6\times 106 }{ 7(49-1) } \) = 1 - \(\frac { 636 }{ 7\times 48 } \)
1 - 1.89 = 0.89
High positive correlation.

Calculation of R :
R = \(\frac { 6\sum { { D }^{ 2 } } }{ N({ N }^{ 2 }-1) } \) = 1 - \(\frac { 6(96) }{ 10(100-1) } \) = 0.4181

P.E. = 0.6745\(\left[ \frac { 1-{ r }^{ 2 } }{ \sqrt { n } } \right] \)= 0.6745 \(\frac { 1-(-0.6{ ) }^{ 2 } }{ \sqrt { 64 } } \) = \(\frac { 0.6745-0.64 }{ 8 } \) = 0.57

Zero correlation

Perfect Negative Correlation

(a) r = 1 means it is perfect positive correlation.
(b) r = - 1means there is perfect negative correlation.
(c) r = 0 means there is no correlation.

For this, we should collect the data. There after we can use any of the following method to find correlation:
(a) Scatter plot
(b) Karl Pearson's coefficient .ofcorrelation. This method is preferable but relatively difficult.

For this we should collect the data. Thereafter we can use any of the following methods to find correlation:
(a) Scatter plot
(b) Karl Pearson's coefficient of correlation, This method is preferable but relatively difficult.

The coefficient of correlation lies between ± 1. If it lies beyond, ± 1, then the relationship between variables is not linear. It is .non linear. Therefore, while interpreting such a value, we must remember, it must have some errors or mistakes

The sign of covariance between X and Y determines the sign of the correlation coefficient. The standard deviations are always positive. When covariance is zero, correlation is also zero. Correlation is preferred to covariance as a measure of association because:
(a) It tells about positive, negative, or zero correlation i.e. no linear correlation.
(b) As well as, r is independent of change of origin and change of scale of measurements.

 r = \(\frac { n(\sum xy)-(\sum x)(\sum y) }{ \sqrt { n(\sum x2-(\sum x)2[n\sum y2-(\sum y)2] } } \)
r = \(\frac { 6(0)-(-2)\times (28) }{ \sqrt { 6(28)-({ -2) }^{ 2 }(6(196)-{ (28) }^{ 2 } } } \)
r = \(\frac { -56 }{ \sqrt { 52\times 392 } } \)
r = \(\frac { -56 }{ \sqrt { 20384 } } \)