The Limitations of Standard Deviation as a Measure of Data Variability: Sensitivity to Outliers, Assumption of Normal Distribution, and Difficulty in Comparison

What is a disadvantage of Standard Deviation?

One disadvantage of the standard deviation is that it can be highly influenced by outliers

One disadvantage of the standard deviation is that it can be highly influenced by outliers. An outlier is a data point that is significantly different from the rest of the data. These extreme values can greatly affect the average distance of data points from the mean, resulting in a larger standard deviation.

For example, let’s say we have a dataset of exam scores: 90, 85, 95, 93, and 30. The mean score is 78.6, and the standard deviation is 25.6. However, if we remove the outlier of 30 from the dataset, the mean becomes 90.6, and the standard deviation reduces to 4.9. In this case, the presence of the outlier drastically increased the standard deviation, making it less representative of the majority of the data.

Another disadvantage of the standard deviation is that it may not provide a complete picture of the spread of data if the distribution is not perfectly symmetrical or follows a normal distribution. It assumes that the data is normally distributed, but if the data is skewed or has long tails, the standard deviation may not accurately capture the variability.

Moreover, the standard deviation is a measure of absolute dispersion, meaning it is expressed in the same units as the original data. This can make it challenging to compare the standard deviations of datasets that have different original units.

In conclusion, while the standard deviation is a widely used measure of dispersion, it has the disadvantage of being sensitive to outliers, assuming normal distribution, and not being easily comparable across different datasets with different units of measurement.

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