Magnitude (mathematics) their magnitudes is called a norm. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. Not all vector spaces are normed. In a pseudo-Euclidean space, the magnitude of a vector is the value of the quadratic form for that vector. When comparing magnitudes, a logarithmic scale is often used. Examples include the loudness of a sound (measured in decibels), the brightness of a star, and the Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. It is not meaningful to simply add or subtract them. Orders of magnitude denote differences
Rating scale at the ordinal level. Numbers indicate the relative position of items, but not the magnitude of difference. Attitude and opinion scales are usually ordinal; one example is a Likert response scale: Some data are measured at the interval level. Numbers indicate the magnitude of difference between items, but there is no absolute zero point. A good example is a Fahrenheit/Celsius temperature scale where the differences between numbers matter, but placement of zero does not. Some data are measured at the ratio level. Numbers indicate magnitude of difference and there is a fixed zero point. Ratios can be calculated. Examples include