Question

Why is one half of the Box wider than the other half of the box

Answer 1

The answer is In its simplest form, the boxplot presents five sample statistics - the minimum, the lower quartile, the median, the upper quartile and the maximum - in a visual display. The box of the plot is a rectangle which encloses the middle half of the sample, with an end at each quartile. The length of the box is thus the interquartile range of the sample. The other dimension of the box does not represent anything in particular. A line is drawn across the box at the sample median. Whiskers sprout from the two ends of the box until they reach the sample maximum and minimum. The crossbar at the far end of each whisker is optional and its length signifies nothing. The following diagram shows a dotplot of a sample of 20 observations (actual sample values used in the display) together with a boxplot of the same data.
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Answer 2

The answer is In its simplest form, the boxplot presents five sample statistics - the minimum, the lower quartile, the median, the upper quartile and the maximum - in a visual display. The box of the plot is a rectangle which encloses the middle half of the sample, with an end at each quartile. The length of the box is thus the interquartile range of the sample. The other dimension of the box does not represent anything in particular. A line is drawn across the box at the sample median. Whiskers sprout from the two ends of the box until they reach the sample maximum and minimum. The crossbar at the far end of each whisker is optional and its length signifies nothing. The following diagram shows a dotplot of a sample of 20 observations (actual sample values used in the display) together with a boxplot of the same data.