Question

The standard deviation is a measure of spread. For datasets with a high standard deviation, the mean is usually less reliable as a measure of central tendency. We know that outliers effect the mean. We express that by saying: the mean is sensitive to outliers. Would you say that the standard deviation is also sensitive to outliers? How might you justify your answer?

Answer 1

The standard deviation is a measure that measures the dispersion of a dataset relative to its mean.

Standard deviation is the square root of variance.

Variance is the average squared deviation of each number from the mean.

Thus, if outliers are present the dispersion/deviation is high, hence the standard deviation is high.

One outlier value can largely affect the results of the standard deviation. The more extreme the outlier, the more the standard deviation is affected.

Hence, Yes the standard deviation is also sensitive to outliers.

e.g.

Consider the sample data values

5, 4, 6, 3, 2, 34, 5, 6, 8, 7

Here, 34 is an outlier

Standard Deviation including 34 = 9.3095

Standard Deviation excluding 34 = 5.1111

Thus, we can see the standard deviation is high when outlier is included