### Definition

In statistics, the statistical data whether qualitative or
quantitative, are generated or obtain through some measurement or some
observational process. Measurement is essentially the task of assigning numbers
to observations according to certain rules. The way in which the numbers are
assigned to observations determines the scale of measurement being used. There are
four level of measurements in statistics. They are-

- Nominal Level
- Ordinal Level
- Interval Level
- Ratio Level

### Nominal Level of Measurement

All qualitative measurements are nominal, regardless of whether the categories are designed by names (male, female) or numerals (bank account no., id no etc.). In nominal level of measurement, the categories differ from one another only in names. In other words, one category of a characteristic is not higher or lower, greater or smaller than the other category. For example, gender (male or female), religion (Muslim, Hindu or others), etc. The nominal level of measurement gives rise to nominal data.

We
must ensure that the categories of nominal level of measurement must be follow
some important properties. They are-

- The categories are must be homogeneous.
- The categories are mutually exclusive and exhaustive.

### Ordinal level of Measurement

In ordinal level of measurement there exist an ordered relationship among the categories. For example, we use less, more, higher, greater, lower etc. for define the categories such as costly, less profitable, more difficult etc. More precisely, the relationships are expressed in terms of the algebra of inequalities: a less than b (a<b) or is greater than b (a>b). So, the socio-economic status (low, medium, high), academic performance (poor, good, very good), agreement on some issue (strongly disagree, disagree, agree, strongly agree) are some practical variable of ordinal level of measurement. Ordinal level of measurement gives ordinal data.

Ordinal
level maintains some important properties as,

- The categories are distinct, mutually exclusive and exhaustive.
- The categories are possible to be ranked or ordered.
- The distance from one category to the other is not necessarily constant.

### Interval Level of Measurement

The interval level of measurement includes all the
properties of the nominal and ordinal level of measurement but it has an
additional property that the difference (interval) between the values is known
and constant size. In this measurement 0 is used as an arbitrary point. The
interval measurement scale has some important properties. They are-

- The data classifications are mutually exclusive and exhaustive.
- The data can be meaningfully ranked or ordered.
- The difference between the categories is known and constant.

For example, in Gregorian calendar 0 is used to separate
B.C. and A.D. We refer to the years before 0 as B.C. and to those after 0 as A.D.
Incidentally 0 is a hypothetical date in the Gregorian calendar because there
never was a year 0.

Another example, a thermometer
measures temperature in degrees, which are of the same size at any point of the
scale. The difference between 20^{0}C and 21^{0}C is the same
as the difference between 12^{0}C and 13^{0}C. The temperature
12^{0}C, 13^{0}C, 20^{0}C, 21^{0}C can be
ranked and the differences between the temperatures can easily be determined. When
the temperature is 0^{0}C, it means not the absence of heat but it is
cold. In fact, 0^{0}C is equal to 32^{0}F.

### Ratio level of Measurement

In ratio level, there is an ordered relationship among the
categories where exist an absolute zero and follow the all properties of
nominal level of measurement. All quantitative data fall under the ratio level
of measurement. For example, wages, stock price, sales value, age, height,
weight, etc. are the real life variable of ratio level measurement. If we say
the sales value is 0, then there is no sale.

There exist some important properties in this level. They
are-

- The categories are mutually exclusive and exhaustive.
- The categories can be ordered or ranked.
- The differences among the categories are constant.
- There exist an absolute zero point.

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