So, mathematicians settled in a number in the middle.Ĭomparing petal length for the Iris dataset. The multiplying factor is 1.5, because any number greater than that would result in a range bigger than 3 standard deviations. Which ends up being approximately 3 standard deviations from the mean. These represent the lower and upper bounds of the area in the distribution that is not considered extreme. To check if a data point is an outlier and check if it falls farther than three standard deviations, we calculate: So any data point that is seen farther than three standard deviations is considered extreme. Only very few data points will be beyond three standard deviations from the mean, more precisely, only 0.3% of the data points.
99.7% of the data is within three standard deviations from the mean.95% of the data is within two standard deviations from the mean,.68% of the data is within one standard deviation above or below the mean,.Max, maximum value in the dataset, excluding outliers, which corresponds to Q3+ 1.5xIQR.Min, minimum value in the dataset excluding outliers, which corresponds to Q1–1.5xIQR.Expressed mathematically, we have IQR = Q3 - Q1. Interquartile range (IQR), the width between the third and first quantiles.Median, the mid-point in the distribution, which also corresponds to the 50th percentile.
Quantiles, specifically the first and third quantiles, which correspond to the 25th and 75th percentiles.
The summary metrics we can extract from a boxplot are: And while we can visualize the shape of the distribution with an histogram, a boxplot highlights the summary metrics that give the distribution its shape. With a boxplot, we can extract the same insights as with an histogram. That’s why we’re so comfortable interpreting the insights of an histogram, where we can spot the values where most data is concentrated around, and we can see the shape of the distribution. We are used to think in terms of frequency and comparing proportions. Histograms highlight frequency while boxplots highlight the range of the data.
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