How Do Outliers Impact Measures of Variability?

📊📈🔍 Hey guys, let’s talk about measures of variability! 📊📈🔍

When there are extreme values in a data set, measures that are less sensitive to those outliers are preferred. One such measure is the Interquartile Range (IQR), which looks at the difference between the first and third quartiles and ignores the minimum and maximum values. The IQR is a better measure of variability than the range, variance, and standard deviation when there are extreme values.

The variance, range, and standard deviation are all based on the distance between each data value and the mean. When there are extreme values in the data set, those values can skew the mean and make these measures less meaningful.

The Mean Absolute Deviation (MAD) is a measure of variability that doesn’t square the distance from the mean like the variance and standard deviation do. This means that extreme values have less impact on the MAD than they do on the variance and standard deviation.

The range is sensitive to outliers because it’s based on the difference between the minimum and maximum values in a data set. When there are outliers, those extreme values can greatly affect the range and make it less meaningful as a measure of variability.

💡 And there you have it! Depending on the data set, certain measures of variability may be more appropriate than others. 💡