Criticism
The sample mean and sample covariance are widely used in statistics and applications, and are extremely common measures of location and dispersion, respectively, likely the most common: they are easily calculated and possess desirable characteristics.
However, they suffer from certain drawbacks; notably, they are not robust statistics, meaning that they are sensitive to outliers. As robustness is often a desired trait, particularly in real-world applications, robust alternatives may prove desirable, notably quantile-based statistics such the sample median for location, and interquartile range (IQR) for dispersion. Other alternatives include trimming and Winsorising, as in the trimmed mean and the Winsorized mean.
Read more about this topic: Sample Mean And Sample Covariance
Famous quotes containing the word criticism:
“I, with other Americans, have perhaps unduly resented the stream of criticism of American life ... more particularly have I resented the sneers at Main Street. For I have known that in the cottages that lay behind the street rested the strength of our national character.”
—Herbert Hoover (1874–1964)
“Parents sometimes feel that if they don’t criticize their child, their child will never learn. Criticism doesn’t make people want to change; it makes them defensive.”
—Laurence Steinberg (20th century)
“A tailor can adapt to any medium, be it poetry, be it criticism. As a poet, he can mend, and with the scissors of criticism he can divide.”
—Franz Grillparzer (1791–1872)