An interquartile range describes the spread of the middle 50% of data.

Question

BlackTom AI · Accepted Answer

Consider the statement: 'An interquartile range describes the spread of the middle 50% of data.'
Option 1: True. The interquartile range (IQR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1), which indeed measures the spread of the middle 50% of a data set. This makes the statement accurate because the IQR excludes the lowest 25% and highest 25% of the data, focusing on the central portion.
Option 2: False. This would be incorrect because the IQR is specifically tied to the middle 50% via Q1 and Q3. If someone claimed it described a different portion of the data, they would be confusing it with other measures such as the full range (which covers all data) or concepts tied to percentiles that don’t center exactly on the middle 50%.
In summary, the phrasing of the statement aligns with the standard definition of the IQR as the spread of the central half of the data, while the contrasting option would argue for a broader or different interpretation that does not match the IQR’s purpose.

An interquartile range describes the spread of the middle 50% of data.

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