High Outliers: All values greater than Q3 + (1.5 × IQR).Low Outliers: All values less than Q1 - (1.5 × IQR).You can calculate outliers mathematically using these rules: They are plotted as single dots on a boxplot. In other words, they “lie outside” most of the data. Outliers are data points that differ significantly from most of the other points in the dataset. In other words, it tells us the width of the “box” on the boxplot.īox plots show outliers in the dataset. The IQR tells us the range of the middle 50% of the data. For example if true location = 2.75, fraction% = 0.75īox plots (also known as box and whisker plots) provide a visualization that provide three key benefits compared to other visualization of data:īox plots show the size of the center quartiles and the values of Q1, Q2, and Q3.īox plots show the interquartile range (commonly called the IQR), a measure of the spread of the data. Fraction% represents the decimal component of the true location. In the formula above, low # represents the number to the left of the true location and high # represents the number to the right of the true location.After finding the true location, we can use the following formula to calculate Q1 and Q3:.True Location = (# of data points - 1) X percentile of interest.Instead we use the following formula first to find the true location: Calculating Q1 and Q3: To find Q1 and Q3, we can't just take the midpoint of two data points.Calculating Q2: To find Q2, all we have to do is calculate the median of the data.Visually, we can see the data split into the four quartiles by the Q1, Q2 and Q3: Frequency histogram of a difficult exam. This means that at Q3, there is 75% of the data below that point. Q3, the end of the third quartile, is the 75 th-percentile.This means that at Q2, exactly half of the data is at or below that point (and exactly half is at or above). Q2, the end of the second quartile, is the 50 th-percentile (which is also the median).This means that at Q1, there is 25% of the data below that point. Q1, the end of the first quartile, is the 25 th-percentile.The points where the quartiles are split have specific names: QuartilesĪll sets of numeric data can be broken up into quartiles, or four equal sized segments that each contain exactly a quarter (25%) of the data. Box plots divide the data into equally sized intervals called quartiles. Just like histograms, box plots (also known as box and whisker plots) are a way to visually represent numeric data.
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