Which of the followings are true in case of the measures of dispersion and central tendency ? A.…
The median minimises the sum of absolute deviations, so mean deviation is least when taken about the median (B); variance is an average of squared deviations and cannot be…
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Which of the followings are true in case of the measures of dispersion and central tendency ?
A. Algebraic sum of deviations from mean is minimum
B. Mean deviation is least when calculated from median
C. Variance is always non-negative
D. Mean, standard deviation and coefficient of variation have same units
E. Relative measures of dispersion are independent of units of measurement
Answer and explanation
Correct answer D
The median minimises the sum of absolute deviations, so mean deviation is least when taken about the median (B); variance is an average of squared deviations and cannot be negative (C); and relative measures such as the coefficient of variation are ratios, free of units (E). Statement A is false because the algebraic sum of deviations from the mean is zero, not a minimum; it is the sum of squared deviations that is least about the mean. Statement D is false because the mean and standard deviation share the data's units while the coefficient of variation has none.
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UGC NET Economics