Which of the following is/are true?
I. There are as many values above the mode as below it.
II. The sum of the differences between the observations in a sample and the mode of the sample equals zero.
III. The mode is not affected by "outliers."
IV. A sample has a unique mode.
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A. B. C. D. E. F.Explanation
A sample can have multiple modes, corresponding to all the numbers which appear with the maximum frequency. Note that the mode is not affected by outliers unless an extreme value occurs frequently. In such a case, it is likely that the observed data contain large errors and hence, it must be reexamined. (I) holds for the median not the mode i.e. there are as many values above the median as below it. (II) holds for the mean i.e. the sum of the differences between the observations in a sample and the mean of the sample equals zero.