Final answer:
The IQR is preferred over standard deviation for skewed data or data with outliers. Mean and standard deviation are advantageous when the data is symmetrical. Outliers may require different actions based on the context of the data.
Step-by-step explanation:
One might prefer the Interquartile Range (IQR) over the standard deviation when the data is skewed or contains outliers, as IQR is less sensitive to extreme values than standard deviation. The mean and standard deviation have the advantage of being measures that take into account all the values in the data set, providing a sense of the overall distribution when the data is symmetric and mound-shaped.
To identify outliers in the data using IQR, calculate the IQR (which is the difference between the third and first quartile, Q3 and Q1, respectively) and then find 1.5 * IQR above Q3 and 1.5 * IQR below Q1. Values that fall outside this range are considered outliers. If a value is identified as an outlier, the appropriate action depends on the context, but it might include investigating the cause of the outlier, using robust statistical methods that are less affected by outliers, or removing it from the data set if it is an error.
Determining whether data values are farther than two standard deviations from the mean requires computing the standard deviation and then adding and subtracting two standard deviations from the mean. This criterion is appropriate for symmetric, mound-shaped data. Parts a and c give different answers if the data is skewed or contains outliers that significantly affect the standard deviation.