Which is not true about Q3?

Question

BlackTom AI · Accepted Answer

Question: Which is not true about Q3?

Option provided: 'It is the mean of the ordered list of observations that are to the right of the median.'

Analysis: To assess this statement, recall that Q3, or the third quartile, is defined as the value below which 75% of the data fall. In most common definitions, Q3 corresponds to the 75th percentile, not to any kind of average of the upper half.

Regarding the phrase 'mean of the ordered list of observations to the right of the median': this would describe a central tendency measure (the average) of the upper portion of the data, not the standard definition of Q3. The quartile concept focuses on a positional value (the cutoff point at which 75% of observations are at or below it), rather than the arithmetic mean of the upper half.

Therefore, this statement mischaracterizes Q3 by equating it with the mean of the upper half, which is not its defining property. It conflates a percentile with a mean statistic and ignores the percentile-based interpretation of Q3.

As for the rest of the options: since no other options are provided in the list, we cannot evaluate them here. If there were additional statements, we would examine each one to determine whether it aligns with the standard understanding that Q3 is the 75th percentile (the value below which 75% of data fall) and differs from the mean of the upper half.

STAT 1450.02 SP2025 (28132) Checkpoint 2.4

Which is not true about Q3?

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