Review Question - QID 103884

The mode of a dataset is the descriptive statistic with the least sensitivity to outliers.

In this study of a new biomedical device the sample size is relatively small. Small datasets are more sensitive to extreme values because each individual extreme value constitutes a larger proportion of the total observations. In this example, a single patient failed to achieve the therapeutic outcome of interest and as such is skewing the distribution of the data.

Rosner provides one commonly accepted definition of an outlier: an observation that is more than 1.5 x IQR away from the median, where IQR is the interquartile range, i.e. the difference between the 75th and 25th percentiles. Extreme outliers are further defined as observations that fall beyond a distance of 3 IQRs from the median.

Rosner also defines the mode as the most frequently occurring value among all the observations in a sample. In cases where no observations share values, there is no mode. If there is more than one most commonly occurring value, there are as many modes as most commonly occurring values. For example, in the set 1,3,3,5,5,6 both 3 and 5 are considered the mode. Because the mode is dependent only on the most frequent observation value, it is entirely insensitive to outlying values.

Illustration A depicts how skewness or outlying values affect the mean median and mode. Notice that the mode never leaves the tallest hump of the distribution; it is entirely insensitive to outlying values.

Incorrect Answers:
Answer 1: The mean is sensitive to outlying values, hence this outlying value's effect on the outcome of this study (which most likely compared the means).
Answer 2: The median is less sensitive to outliers than the mean but more sensitive than the mode (see Illustration A).
Answer 4 and 5: The standard deviation is the square root of the variance and both are more sensitive to outliers than the mean.