outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits Lower limit: Q-1.5 x (IQR) Upper limit: Q3 + 1.5 x (IQR) where IQR is the interquartile range, are suspected outliers. In the computer software package Minitab, values beyond these limits are plotted with asterisks (*). Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were as follows. 66 73 69 63 61 56 74 70 51 64 60 73 68 68 73 51 5 74 68 63 67 81 65 64 (a) Make a box-and-whisker plot of the data. 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 (b) Find the value of the interquartile range (IQR). IQR = (c) Multiply the IQR by 1.5 and find the lower and upper limits. lower limit upper limit (d) Are there any data values below the lower limit? Yes No Are there any data values above the upper limit? Yes No List any suspected outliers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) What might be some explanations for the outlier(s)? There is a single outlier, but it is possible this student is just far below average height. There are multiple outliers, but they are all likely to be errors. There are multiple outliers, but it is possible these students are just far above average height. There is a single outlier, but it is most likely an error. cted outliere in this data