Solved – Variance/standard deviation versus interquartile range (IQR)

interquartilevariabilityvariance

Variance and interquartile range (IQR) are both measures of variability.

But IQR is robust to outliers, whereas variance can be hugely affected by a single observation.

Since variance (or standard deviation) is a more complicated measure to understand, what should I tell my students is the advantage that variance has over IQR?

Best Answer

The main use of variance is in inferential statistics.

So, variance and standard deviation are integral to understanding z-scores, t-scores and F-tests.

This means that when your data are normally distributed, the standard deviation is going to have specific properties and interpretations. When your data are not normal (skewed, multi-modal, fat-tailed,...), the standard deviation cannot be used for classicial inference like confidence intervals, prediction intervals, t-tests, etc., and cannot be interpreted as a distance from the mean.

You can say things like "any observation that's 1.96 standard deviations away from the mean is in the 97.5th percentile." if your data are normally distributed.