is standard deviation resistant to outliers?
The correct answer and explanation is:
Correct Answer: No, standard deviation is not resistant to outliers.
Standard deviation is a measure of the spread or dispersion of a set of data points around the mean. It is calculated using the squared differences between each data point and the mean. Because of this mathematical structure, standard deviation is highly sensitive to values that are far from the average.
When an outlier is introduced into a data set, it increases the average distance between the data points and the mean. Since these distances are squared in the standard deviation formula, even a single extreme value can cause a significant increase in the overall result. For example, in a data set like [4, 5, 6, 7, 100], the value 100 is an outlier. It causes both the mean and the standard deviation to increase noticeably compared to a more uniform set like [4, 5, 6, 7, 8].
This sensitivity makes standard deviation a non-resistant statistic. Resistant measures are those that are not greatly influenced by outliers or skewed data. For instance, the median and interquartile range (IQR) are resistant measures because they are based on the position of values rather than their actual magnitudes.
In situations where data may contain outliers or is not normally distributed, relying solely on the standard deviation can lead to misleading conclusions about variability. In such cases, alternative measures like the IQR may provide a more accurate picture of the data’s spread.
Therefore, standard deviation is a useful tool for measuring variability in data, but it should be used with caution when outliers are present, as it is not resistant to their influence.