試題詳解

29. (5%) A histogram of a dataset X is plotted in Figure (i). The 1st quartile, median and the 3'd quartile of the data are 10, 25, and 50. Which of the following statements is correct? i)
(A) The truncated mean of the central 50% data should be (10+50)/2=30
(B) If another variable Y is positively correlated with X, the distribution of Y must be skew to the right as the distribution of X
(C) The mode is greater than 25
(D) Since it is a skewed distribution, we can model the data with a x distribution
(E) Suppose we randomly draw 30 samples with replacement from this dataset and take average to get X. The distribution of X is more likely to be the function f3(x) in Figure (ii) rather than the function f1(x) or f2(x) 110 130