Question

Problem Set 6:

a) The variance is high if the mean is a good measure for central tendency.

b) If the covariance of X and Y is close to −1, then there is a weak negative

relationship between X and Y .

c) The standard deviation of X is always greater than or equal to the variance

of X.

d) The covariance of X and Y is always smaller than or equal to the correlation coefficient of X and Y .

Answer 1

a) This statement is FALSE. If mean is a good measure of central tendency, then the variance should be minimum. Smaller the variance, better the measure of central tmedency.

b) This statement is true. Covariance of X and Y is -1, and the presence of sum of squares in denominator will make the expression small. And hence weak negative correlation.

c) FALSE. Variance is square of Standard Deviation. Hence, Variance is greater than or equal to Standard Deviation always.

d) Partially true partially false. Correlation is greater than covariance only when covariance is negative. Otherwise, Correlation is less rhan Covariance.