Degrees of freedom refer to the number of independent values or quantities that can vary in a statistical analysis or mechanical system. In statistics, it often indicates the number of values that are free to vary when calculating a statistic, such as the mean. For example, in a dataset with five values, if four are known, the fifth is determined, giving it four degrees of freedom. In mechanics, degrees of freedom describe the number of independent movements an object can make. For instance, a robotic arm may have multiple joints, each allowing rotation or movement in different directions, contributing to its overall degrees of freedom.