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In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [ 1 ] The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. [ 2 ][ 3 ][ 4 ] To calculate the IQR, the ...
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
The fences are sometimes also referred to as "whiskers" while the entire plot visual is called a "box-and-whisker" plot. When spotting an outlier in the data set by calculating the interquartile ranges and boxplot features, it might be easy to mistakenly view it as evidence that the population is non-normal or that the sample is contaminated.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered ...
Simple L-estimators can be visually estimated from a box plot, and include interquartile range, midhinge, range, mid-range, and trimean. In statistics, an L-estimator (or L-statistic) is an estimator which is a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number ...
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: the sample minimum (smallest observation) the lower quartile or first quartile. the median (the middle value) the upper quartile or third quartile. the sample maximum (largest observation)
Quantile. Probability density of a normal distribution, with quantiles shown. The area below the red curve is the same in the intervals (−∞,Q1), (Q1,Q2), (Q2,Q3), and (Q3,+∞). In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or ...
where is the interquartile range of the data and is the number of observations in the sample . In fact if the normal density is used the factor 2 in front comes out to be ∼ 2.59 {\displaystyle \sim 2.59} , [ 4 ] but 2 is the factor recommended by Freedman and Diaconis.