Question

I want to know the answer and explanation of (d) and (f).

2. Percentiles and Quartiles Given a data set with n data values yvi < /2 ..S yn, define the pth percentile of the data set to be the element at index ceiling, and it means that we always round up to the next integer. For example, suppose we have a data set with n - 13 elements, and we want to calculate the 25th percentile of the data set. Then since p* n 100 The notation is called 25 * 13 13 100 3.25] -4, we know that the 25th percentile of the data is the element y4 Define the quartiles of the data set as follows : . The first quartile Q1 is the 25th percentile of the data set. » The second quartile Q2 is the 50th percentile of the data set. » The third quartile Q3 is the 75th percentile of the data set. True or false? True means that the statment is true for all data sets. False means that the statement can sometimes be false. Justify your answers, based on the definitions above (a) Qi 〈 Q2 〈 Q3 (b) Q1 < Q2 S Q3 (c) The average of the the first and third quartiles is the second quartile. (d) The 50th percentile is the median. (e) If p f q, then the pth percentile is not the same as the qth percentile Q3-Q1 is a measure of dispersion.

Answer 1