For example, if the smallest value and the first quartile were both one, the median and the third quartile were both five, and the largest value was seven, the box plot would look like: Figure 2.1.1.4 The right side of the box would display both the third quartile and the median. In this case, the diagram would not have a dotted line inside the box displaying the median. For instance, you might have a data set in which the median and the third quartile are the same. The following data are the number of pages in 40 books on a shelf. The middle 50% (middle half) of the data has a range of 5.5 inches.The interval 59–65 has more than 25% of the data so it has more data in it than the interval 66 through 70 which has 25% of the data.There are two potential outliers in distribution A.= 70 - 64.5 = 5.5\). According to the definition used by the function in R software, all values higher than Q3 + 1.5 x (Q3 - Q1) = 0.32 + 1.5 x 0.30 = 0.77 are outside the right whisker and indicated by a circle. The distribution C is negatively skewed because the whisker and half-box are longer on the left side of the median than on the right side.Īll three distributions include potential outliers. The centre of distribution C is the highest of the three distributions (median is 0.88).It’s the most concentrated distribution because the interquartile range is 0.21, compared to 0.30 for distribution A and 0.26 for distribution C. Distribution B is approximately symmetric, because both half-boxes are almost the same length (0.11 on the left side and 0.10 on the right side).The distribution is positively skewed, because the whisker and half-box are longer on the right side of the median than on the left side. The centre of distribution A is the lowest of the three distributions (median is 0.11).The information is grouped by Measurement (appearing as row headers), Distribution A, Distribution B and Distribution C (appearing as column headers). This table displays the results of Data table for chart 4.5.2.1. Example 1 – Comparison of three box and whisker plots Data points that are outside this interval are represented as points on the graph and considered potential outliers. That is, the whisker reaches the value that is the furthest from the centre while still being inside a distance of 1.5 times the interquartile range from the lower or upper quartile. The box and whisker plot can be presented horizontally, like in figure 4.5.2.1, or vertically.Ī variation of the box and whisker plot restricts the length of the whiskers to a maximum of 1.5 times the interquartile range. The graph is usually presented with an axis that indicates the values (not shown on figure 4.5.2.1).The whiskers are the two lines outside the box, that go from the minimum to the lower quartile (the start of the box) and then from the upper quartile (the end of the box) to the maximum.Sometimes, the mean is also indicated by a dot or a cross on the box plot. The vertical line that split the box in two is the median.The box covers the interquartile interval, where 50% of the data is found.
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