The tails are the extremities of the sample or The Boxplot as an Indicator of Tail Length The top whisker and the line is rising to the top of the box. The boxplot of a sample of 20 points from a population which is skewed to the left. Is much longer than the bottom whisker and the line is gravitating towards the bottom of the box. The boxplot of a sample of 20 points from a population which is skewed to the right. The line is close to the centre of the box and The boxplot of a sample of 20 points from a symmetric population. The boxplot of a sample of 20 points from a population centred on 10 with standard deviation 3. The boxplot of a sample of 20 points from a population centred on 10 with standard deviation 1. The boxplot of a sample of 20 points from a population centred on 12. The boxplot of a sample of 20 points from a population centred on 7. The Boxplot as an Indicator of Centrality This is all important whenĬonsidering appropriate analyses of the data. The 'shape' of the sample, and by implication, the shape of the The number of points in the sample is not too small, the boxplot also Population and short whiskers, a short tailed population. Whiskers, relative to the box length, can betray a heavy tailed Tells us whether the sample is symmetric or skewed, either to the right or left. The position of the box in its whiskers and the position of the line in the box also The box length gives an indication of the sample variability and the line across the box Particularly when the boxplots of several samples are lined up alongside one another ( Parallel Boxplots).

Much more can be read from a boxplot than might be surmised from the simplistic method of its construction, The width across the page signifies nothing. The length of the box becomes its height. Most statistical packages seem to produce them vertically by default, as shown on the right, rather than horizontally. The following diagram shows a dotplot ofĪ sample of 20 observations ( actual sample values used in the display) together withĪlthough boxplots can be drawn in any orientation, TheĬrossbar at the far end of each whisker is optional and its length Of the box until they reach the sample maximum and minimum. A line is drawnĪcross the box at the sample median. Of the box does not represent anything in particular. Of the plot is a rectangle which encloses the middle half of the sample, with an end at each quartile. In its simplest form, the boxplot presents five sample statistics - the minimum,

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