Interpreting IQR as a Measure of Risk
A researcher compared daily stock prices over a five-year period using parallel boxplots. The researcher observed that the interquartile range (IQR) for the year 2021 was smaller than the IQR for the year 2018 and concluded that the stock’s risk had decreased. Which of the following describes the primary flaw in the researcher’s conclusion?
While a smaller IQR indicates reduced dispersion among the middle 50% of values, it does not account for variability in the tails. Risk should be assessed using overall volatility, not just the IQR.
There is no mistake; a smaller IQR definitively shows reduced overall risk.
The researcher miscalculated the IQR; in fact, the IQR in 2021 is larger than in 2018.
The error is in focusing on the median stock price, which is irrelevant for assessing risk.
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