If it is set to 2, for example, the inner fence will be from the lower and upper hinges to 2 times the box length the mild outliers' range will be from 2 to 4 times the box length beyond the hinges, and the extreme outliers will be values that are more than 4 times the box length. Changing the Length parameter will affect the length of the whiskers and how the outliers are classified. The mild and extreme outliers have different symbologies applied to distinguish them. Said another way, the mild outliers are those that occur between 1.5 and 3 times the box length away from the lower and upper hinges, and the extreme outliers are those that occur beyond 3 times the box length away from the lower and upper hinges. The extreme outliers are those that occur beyond the outer fence. The mild outliers are those that occur in the region from the inner fence to the outer fence. The region from one step length to two step lengths away from the lower and upper hinges is the outer fence. The outliers are classified into two groups, mild outliers and extreme outliers. Outliers Outliers are values that occur beyond the inner fence, or the step length (1.5 times the box length) away from the lower and upper hinges. The whiskers will only extend from the lower and upper hinges to the smallest and largest data values within the inner fence, respectively. The region one step length beyond the lower and upper hinges is called the inner fence. The default length value is 1.5, which is 1.5 times the box length (IQR). The Length parameter is often referred to as step in the literature. The maximum possible extent of the whiskers is set by the Length parameter. Whisker The lines extending out from the box are called whiskers. The upper hinge is the largest data value that is smaller than the third quartile. Specifically, the lower hinge is the smallest data value that is larger than the first quartile. The lower and upper edges of the box, known as hinges, are approximately determined by the first and third quartiles. The difference between the upper and lower quartiles is known as the interquartile range (IQR) and is a measure of the variability of the data. The box contains the middle 50 percent of the data points. Box The horizontal line contained within the box marks the median value (second quartile) of the data. The quartiles correspond to the 25th, 50th, and 75th percentiles. The portions of data below and above the median have their own medians determined, respectively yielding the second and third quartiles. The second quartile of the data is commonly known as the median. The first, second, and third quartiles of the data values are determined. Box plots are also known as Box Whisker plots. It shows as a graphic summary the median (location), spread (dispersion), skewness, and outliers in the data. The single points on the diagram show the outliers.Box plots are a succinct method for displaying the statistical distribution of values in data. The values at which the horizontal lines stop at are the values of the upper and lower values of the data. The right edge of the box shows the upper quartile it shows that $25$% of the data lies to the right of the upper quartile value. The left edge of the box represents the lower quartile it shows the value at which the first $25$% of the data falls up to. This shows that $50$% of the data lies on the left hand side of the median value and $50$% lies on the right hand side. The line splitting the box in two represents the median value. Interpreting a boxplot can be done once you understand what the different lines mean on a box and whisker diagram. These can be displayed alongside a number line, horizontally or vertically. It is a useful way to compare different sets of data as you can draw more than one boxplot per graph. The shape of the boxplot shows how the data is distributed and it also shows any outliers. Contents Toggle Main Menu 1 Definition 2 Reading a Box and Whisker Plot 2.1 Video Examples 3 Constructing a Box and Whisker Diagram 4 Worked Example 4.1 Video Example 4.2 Common Mistakes 5 Workbook 6 Test Yourself 7 External Resources DefinitionĪ box and whisker plot or diagram (otherwise known as a boxplot), is a graph summarising a set of data.
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