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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 data set ...
Quartile. Statistic which divides data into four same-sized parts for analysis. In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic.
Kernel density estimation of 100 normally distributed random numbers using different smoothing bandwidths.. In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights.
IQR and MAD. One of the most common robust measures of scale is the interquartile range (IQR), the difference between the 75th percentile and the 25th percentile of a sample; this is the 25% trimmed range, an example of an L-estimator. Other trimmed ranges, such as the interdecile range (10% trimmed range) can also be used.
Truncate the fractional quartile size, and remove this number from the 1st and 4th quartiles (2.25 observations in each quartile, thus the lowest 2 and the highest 2 are removed). 1, 3, (5), 7, 9, 11, (13), 15, 17. Thus, there are 3 full observations in the interquartile range with a weight of 1 for each full observation, and 2 fractional ...
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For instance, the 10% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% winsorized mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. Winsorizing thus does not change the total number of values in the data set, N.
Here, 1.5 IQR above the third quartile is 88.5°F and the maximum is 81°F. Therefore, the upper whisker is drawn at the value of the maximum, which is 81°F. Similarly, the lower whisker boundary of the box plot is the smallest data value that is within 1.5 IQR below the first quartile. Here, 1.5 IQR below the first quartile is 52.5°F and the ...