Question

a boxplot was constructed for a data set, but it was later discovered that the maximum value was recorded incorrectly. the value 41 was a mistake, should have been 11. ... after making this correction, which quartile shows the greatest spread of data? first quartile (q₁) a, second quartile (q₂) b, third quartile (q₃) c, fourth quartile (q₄) d

Explanation:

To determine which quartile shows the greatest spread, we analyze the quartiles:

• The first quartile (\(Q_1\)) represents the spread of the lower 25% of data.
• The second quartile (\(Q_2\)) is the median, not a spread measure.
• The third quartile (\(Q_3\)) represents the spread of the upper 25% (from \(Q_2\) to \(Q_3\)).
• The fourth quartile (often mis - referred, actually the range from \(Q_3\) to maximum) was affected by the correction (max changed from 41 to 11, reducing the upper spread). But typically, the third quartile's spread (between \(Q_2\) and \(Q_3\)) or the spread related to the upper half. However, in standard quartile spread (IQR is \(Q_3 - Q_1\), but for individual quartile spread: \(Q_2 - Q_1\) (first to second), \(Q_3 - Q_2\) (second to third), and \(Max - Q_3\) (third to fourth). After correcting the max to 11 (which is lower than before), the \(Max - Q_3\) spread is reduced. The third quartile's spread (\(Q_3 - Q_2\)) is usually the largest among the quartile - to - quartile spreads as the upper half of the data (above median) often has more variability or a larger range between median and \(Q_3\) compared to the lower half (between \(Q_1\) and \(Q_2\)).

Answer:

C. Third quartile (\(Q_3\))