APFIVE Interpreting IQR as a Measure of Risk
In a study of daily stock prices over five years, a researcher examines parallel boxplots. Noticing that the interquartile range (IQR) in 2021 is smaller than in 2018, the researcher concludes that the stock’s risk has decreased over time. What is the error in this interpretation?
A
The error is in focusing on the median stock price, which is irrelevant for assessing risk.
B
There is no mistake; a smaller IQR definitively shows reduced overall risk.
C
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.
D
The researcher miscalculated the IQR; in fact, the IQR in 2021 is larger than in 2018.
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