Which of the following statements are true? I. A good measure of dispersion is not duly affected by…
Statements I, III, and IV are true: (I) an ideal measure of dispersion should not be unduly distorted by extreme outliers; (III) the coefficient of determination (R^2) lies…
Choose your answer
Which of the following statements are true?
I. A good measure of dispersion is not duly affected by extreme observations
II. Standard deviation incorporates the effect of extreme values thus making it most reliable measure of dispersion
III. Co-efficient of determination (R2) is always positive and less than one
IV. Non-parametric tests do not require us to make restrictive assumptions about shape of population distribution V. Z-test cannot be applied when population is normal
Answer and explanation
Correct answer A
Statements I, III, and IV are true: (I) an ideal measure of dispersion should not be unduly distorted by extreme outliers; (III) the coefficient of determination (R^2) lies between 0 and 1; and (IV) non-parametric (distribution-free) tests do not require restrictive assumptions about the shape of the population distribution. Statement II is false (sensitivity to extreme values is a demerit of standard deviation), and Statement V is false (the Z-test is specifically designed for normal populations).
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