Astudent counted the number of times her teacher said word like during her class over an 11- day period [likes per class period] 22,19,16,19,23,20,20,21,22,21,14 construct a box plot to represent the data, and determine which of the following is correct about the data set a. q1=13,b. q3=22,c. the interquartile range is 9,d. the median is 21

Let us calculate the median; the 6th observation is 20, so it is 20. We need the 6th observation so that out of the 11 observations we have 5 above the median and 5 below (or equal). We also have that then Q1 is the median of the lowest 5 observations, hence 19 (14,16,19,19,20, the 3rd observation is 19). Similarly, we get that the median for the upper half of the observations, Q3 namely, is 22 (21,21,22,22,23, the 3rd observation is 22). Thus, the interquartile range is 3=Q3-Q1. According to our calculations, all observations are wrong.