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A box plot is a way of organizing numerical data on a single number line, with a box representing the first and third quartiles and whiskers extending to the minimum and maximum values. The five numbers summary and interquartile range are important in creating box plots, which can be used to compare data sets. Box plots do not show data frequency and cannot provide information on mean, mode, or standard deviation. Other graphs may be more useful for these purposes.
A box plot or box-and-whisker plot is a method of organizing numerical data along a single number line, which can be horizontal or vertical. The actual box, when the plot is horizontal, is located slightly above the number line and consists of three vertical lines, connected by horizontal lines. The horizontal bounds of the box represent the first and third quartiles (25th and 75th percentiles), separated by the middle line, which is the median or 50th percentile of the data. On both sides of the box plot from the center of the horizontal lines, vertical lines, sometimes called whiskers, extend. When these reach the minimum and maximum number of the dataset, they end up with smaller horizontal lines, although this can vary slightly depending on the spread of the data.
There are a few important elements that make up a good box plot and some numbers that people need to know when creating these charts. The first of these is called the five numbers summary, often abbreviated as five numbers. sum. This is a list of the first and third quartiles, the median, and the minimum and maximum numbers in the data. In some applications, people will need to list them near the graph, although analyzing a graph with a good number line can also derive these numbers by looking at the three horizontal lines and trailing whiskers. It’s not a chicken/egg question for the person drawing a texture because the five numbers. sum. must be used to create the texture.
People also need to know a number called the interquartile range (IQR). By subtracting the first quartile from the third quartile you get the IQR and using different software or scientific calculators you can also get this number and the summary of the five numbers by entering all the data. The IQR matters because the lines extending from the box usually only extend 1.5 times the IQR. Data beyond that point is indicated by dots instead of a solid line. These points often suggest that the data has outliers.
There are a variety of uses for the box plot. Several graphs can be plotted over a number line and could compare similar data sets that are differentiated by some important factor. For example, scientists or statisticians might record the heart rates of men and women and then construct two stacked box plots to look for significant differences in range and quartiles.
Box plots do not take data frequency into account. The lack of an additional scale (vertical or horizontal) omits information about repeating numbers, the size of the data set, and most individual numbers. The person looking at a box plot will better understand the summary of the five numbers, the range, and whether the data has any outliers. The size of the box, the relationship between median and quartiles, and whisker length can show whether the data is biased, but they can’t tell you about things like mean, mode, or standard deviation. Other graphs like histograms can be more useful when people want to represent things like frequency or get better pictures of the distribution of data.
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