i. in a positively skewed distribution, the mean is always greater than the median. ii. in a negatively…

i. in a positively skewed distribution, the mean is always greater than the median. ii. in a negatively skewed distribution, the mode occurs at the peak of the curve. iii. in a negatively skewed distribution, the mode is greater than the median. a. (i) is a correct statement, but not (ii) or (iii). b. (i), (ii) and (iii) are all false statements. c. (i) and, (ii) are correct statements but not (iii). d. (i) and, (iii) are correct statements but not (ii). e. (i), (ii) and (iii) are all correct statements

i. in a positively skewed distribution, the mean is always greater than the median. ii. in a negatively skewed distribution, the mode occurs at the peak of the curve. iii. in a negatively skewed distribution, the mode is greater than the median. a. (i) is a correct statement, but not (ii) or (iii). b. (i), (ii) and (iii) are all false statements. c. (i) and, (ii) are correct statements but not (iii). d. (i) and, (iii) are correct statements but not (ii). e. (i), (ii) and (iii) are all correct statements

Answer

Brief Explanations:

  1. For statement (i): In a positively skewed distribution, the tail pulls the mean toward the right (higher values), so mean > median > mode. This statement is correct.
  2. For statement (ii): The mode is defined as the most frequent value, which corresponds to the peak of any distribution curve, regardless of skewness. This statement is correct.
  3. For statement (iii): In a negatively skewed distribution, the tail pulls the mean toward the left (lower values), so mode > median > mean. This statement is correct.

Answer:

e. (i), (ii) and (iii) are all correct statements