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 5x 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 a Make a box and whisker plot of the data 0 10 20 30 40 50 60 70 80 90 HI 0 10 20 30 40 50 60 70 80 90 b Find the value of the interquartile range IQR IQR o 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 67 81 65 64 IH 0 10 20 30 40 50 60 70 80 90 Q 0 10 20 30 40 50 60 70 80 90 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 O 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 O 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 That acted outliers in this data