Example: Speed of Light Data
Gelman et al. in Bayesian Data Analysis (2004) consider a data set relating to speed of light measurements made by Simon Newcomb. The data sets for that book can be found via the Classic data sets page, and the book's website contains more information on the data.
Although the bulk of the data look to be more or less normally distributed, there are two obvious outliers. These outliers have a large effect on the mean, dragging it towards them, and away from the center of the bulk of the data. Thus, if the mean is intended as a measure of the location of the center of the data, it is, in a sense, biased when outliers are present.
Also, the distribution of the mean is known to be asymptotically normal due to the central limit theorem. However, outliers can make the distribution of the mean non-normal even for fairly large data sets. Besides this non-normality, the mean is also inefficient in the presence of outliers and less variable measures of location are available.
| This article may contain original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research may be removed. |
Read more about this topic: Robust Statistics
Famous quotes containing the words speed, light and/or data:
“Wait, Kate! You skate at such a rate
You leave behind your skating mate.
Your splendid speed won’t you abate?
He’s lagging far behind you, Kate.”
—David Daiches (b. 1912)
“To the highest leadership among women it is given to hold steadily in one hand the sacred vessels that hold the ancient sanctities of life, and in the other a flaming torch to light the way for oncoming generations.”
—Anna Garlin Spencer (1851–1931)
“Mental health data from the 1950’s on middle-aged women showed them to be a particularly distressed group, vulnerable to depression and feelings of uselessness. This isn’t surprising. If society tells you that your main role is to be attractive to men and you are getting crow’s feet, and to be a mother to children and yours are leaving home, no wonder you are distressed.”
—Grace Baruch (20th century)