Question

10. Expand Your Knowledge: Outliers Some data sets include values so high or so low
that they seem to stand apart from the rest of the data. These data are called 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: Q1  1.5  (IQR)
Upper limit: Q3  1.5  (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
65 72 68 64 60 55 73 71 52 63 61 74
69 67 74 50 4 75 67 62 66 80 64 65
(a) Make a box-and-whisker plot of the data.
(b) Find the value of the interquartile range (IQR).
(c) Multiply the IQR by 1.5 and find the lower and upper limits.
(d) Are there any data values below the lower limit? above the upper limit? List any
suspected outliers. What might be some explanations for the outliers?