Page 80 -

HAN
3:15 Page 43
2011/6/1
09-ch02-039-082-9780123814791
#5
2.1 Data Objects and Attribute Types 43

2.1.5 Numeric Attributes
A numeric attribute is quantitative; that is, it is a measurable quantity, represented in
integer or real values. Numeric attributes can be interval-scaled or ratio-scaled.

Interval-Scaled Attributes
Interval-scaled attributes are measured on a scale of equal-size units. The values of
interval-scaled attributes have order and can be positive, 0, or negative. Thus, in addition
to providing a ranking of values, such attributes allow us to compare and quantify the
difference between values.

Example 2.4 Interval-scaled attributes. A temperature attribute is interval-scaled. Suppose that we
have the outdoor temperature value for a number of different days, where each day is
an object. By ordering the values, we obtain a ranking of the objects with respect to
temperature. In addition, we can quantify the difference between values. For example, a
◦
◦
temperature of 20 C is five degrees higher than a temperature of 15 C. Calendar dates
are another example. For instance, the years 2002 and 2010 are eight years apart.
Temperatures in Celsius and Fahrenheit do not have a true zero-point, that is, neither
◦
◦
0 C nor 0 F indicates “no temperature.” (On the Celsius scale, for example, the unit of
measurement is 1/100 of the difference between the melting temperature and the boiling
temperature of water in atmospheric pressure.) Although we can compute the difference
between temperature values, we cannot talk of one temperature value as being a multiple
◦
of another. Without a true zero, we cannot say, for instance, that 10 C is twice as warm
◦
as 5 C. That is, we cannot speak of the values in terms of ratios. Similarly, there is no
true zero-point for calendar dates. (The year 0 does not correspond to the beginning of
time.) This brings us to ratio-scaled attributes, for which a true zero-point exits.
Because interval-scaled attributes are numeric, we can compute their mean value, in
addition to the median and mode measures of central tendency.

Ratio-Scaled Attributes
A ratio-scaled attribute is a numeric attribute with an inherent zero-point. That is, if
a measurement is ratio-scaled, we can speak of a value as being a multiple (or ratio)
of another value. In addition, the values are ordered, and we can also compute the
difference between values, as well as the mean, median, and mode.

Example 2.5 Ratio-scaled attributes. Unlike temperatures in Celsius and Fahrenheit, the Kelvin (K)
◦
◦
temperature scale has what is considered a true zero-point (0 K = −273.15 C): It is
the point at which the particles that comprise matter have zero kinetic energy. Other
examples of ratio-scaled attributes include count attributes such as years of experience
(e.g., the objects are employees) and number of words (e.g., the objects are documents).
Additional examples include attributes to measure weight, height, latitude and longitude