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:
“A friend of mine spoke of books that are dedicated like this: “To my wife, by whose helpful criticism ...” and so on. He said the dedication should really read: “To my wife. If it had not been for her continual criticism and persistent nagging doubt as to my ability, this book would have appeared in Harper’s instead of The Hardware Age.””
—Brenda Ueland (1891–1985)
“People try so hard to believe in leaders now, pitifully hard. But we no sooner get a popular reformer or politician or soldier or writer or philosopher—a Roosevelt, a Tolstoy, a Wood, a Shaw, a Nietzsche, than the cross-currents of criticism wash him away. My Lord, no man can stand prominence these days. It’s the surest path to obscurity. People get sick of hearing the same name over and over.”
—F. Scott Fitzgerald (1896–1940)
“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)