The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...

Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...

To promote clear communication, for instance, about the location of a patient's abdominal pain or a suspicious mass, anatomists and clinicians typically use imaginary lines to categorize the abdominopelvic cavity into either four quadrants or nine regions to identify organs in the cavity.
The simpler quadrants approach, which is more commonly used in medicine, subdivides the cavity with one horizontal and one vertical line that intersects at the patient's umbilicus (navel). The four...

One influential perspective on what motivates people's behavior is detailed in Tory Higgin's self-discrepancy theory (Higgins, 1987). He proposed that people hold disagreeing internal representations of themselves that lead to different emotional states.  

The center of gravity of a body is an imaginary point where the body's total weight is assumed to be concentrated, and the body is perfectly balanced. The center of the mass of a body is a point at which the whole of the mass of the body appears to be concentrated. If the acceleration due to gravity, g, has the same value at all points on a body, its center of gravity is identical to its center of mass. The center of gravity of homogeneous bodies such as a sphere, cube, or rectangular plate...

Consider a man with a mass of 70 kg seated in a chair connected to a pin support through a member BC. If the man maintains an upright position, the task is to determine the horizontal and vertical reactions of the chair on the man when the member makes a 45° angle with the horizontal. At this moment, the man has a speed of 5 m/s, increasing at a rate of 1 m/s².