## Explain the following terms Population Statistics Constant Variable

Explain the following terms Population Statistics Constant Variable Explain the following terms with examples:

Population

A population is a distinct group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped together by a common feature can be said to be a population.

A sample is a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

Statistics

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting, and presenting empirical data. Statistics is highly interdisciplinary field research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory.

In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools.

Two fundamental ideas in the field of statistics are uncertainty and variation. There are many situations that we encounter in science in which the outcome is uncertain.

In some cases, the uncertainty is because the outcome in question is not determined yet while in other cases the uncertainty is because although the outcome has been determined already we are not aware of it (e.g., we may not know whether we passed a particular exam).

Constant

In mathematics, the word constant can have multiple meanings. As an adjective, it refers to non-variance as a noun, it has two different meanings: A fixed and well-defined number or another non-changing mathematical object. The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. A function whose value remains unchanged. Such a constant is commonly represented by a variable that does not depend on the main variable(s) in question.

Variable

In mathematics, a variable is a symbol and placeholder for (historically) a quantity that may change any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves every quadratic equation by substituting the numeric values of the coefficients of the given equation for the variables that represent them. In mathematical logic, a variable is either a symbol representing an unspecified term of the theory (a meta-variable) or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation.

Data

Although the terms “data” and “information” are often used interchangeably, this term has distinct meanings. In some popular publications, data are sometimes said to be transformed into information when they are viewed in context or in post-analysis. However, in academic treatments of the subject data are simply units of information. Data are used in scientific research, businesses management (e.g., sales data, revenue, profits, stock price), finance, governance (e.g., crime rates, unemployment rates, literacy rates), and in virtually every other form of human organizational activity (e.g., censuses of the number of homeless people by non-profit organizations).

Explain the types of measurement scales with examples.

Nominal, Ordinal, Interval, and Ratio are defined as the four fundamental levels of measurement scales that are used to capture data in the form of surveys and questionnaires, each being a multiple-choice question.

Each scale is an incremental level of measurement, meaning, each scale fulfills the function of the previous scale, and all survey question scales such as Likert, Semantic Differential, Dichotomous, etc, are the derivation of these 4 fundamental levels of variable measurement. Before we discuss all four levels of measurement scales in detail, with examples, let’s have a quick brief look at what these scales represent.

A nominal scale is a naming scale, where variables are simply “named” or labeled, with no specific order. The ordinal scale has all its variables in a specific order, beyond just naming them. The Interval scale offers labels, order, as well as, a specific interval between each of its variable options.  The ratio scale bears all the characteristics of an interval scale, in addition to that, it can also accommodate the value of “zero” on any of its variables.

Nominal Scale: 1st Level of Measurement

Nominal Scale, also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn’t involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as there is no numerical value of the options.

There are cases where this scale is used for the purpose of classification – the numbers associated with variables of this scale are only tags for categorization or division. Calculations done on these numbers will be futile as they have no quantitative significance.

Ordinal Scale: 2nd Level of Measurement

Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables.

These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc. It is quite straightforward to remember the implementation of this scale as ‘Ordinal’ sounds similar to ‘Order’, which is exactly the purpose of this scale.

Ordinal Scale maintains descriptional qualities along with an intrinsic order but is void of an origin of scale and thus, the distance between variables can’t be calculated. Descriptional qualities indicate tagging properties similar to the nominal scale, in addition to which, the ordinal scale also has a relative position of variables. Origin of this scale is absent due to which there is no fixed start or “true zero”.

Interval Scale: 3rd Level of Measurement

Interval Scale is defined as a numerical scale where the order of the variables is known as well as the difference between these variables. Variables that have familiar, constant, and computable differences are classified using the Interval scale. It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities, which is what the Interval scale helps in achieving.

These scales are effective as they open doors for the statistical analysis of provided data. Mean, median or mode can be used to calculate the central tendency in this scale. The only drawback of this scale is that there is no pre-decided starting point or a true zero value.

The Interval scale contains all the properties of the ordinal scale, in addition to which, it offers a calculation of the difference between variables. The main characteristic of this scale is the equidistant difference between objects.

Ratio Scale: 4th Level of Measurement

Ratio Scale is defined as a variable measurement scale that not only produces the order of variables but also makes the difference between variables known along with information on the value of true zero.

It is calculated by assuming that the variables have an option for zero, the difference between the two variables is the same and there is a specific order between the options.

With the option of true zero, varied inferential, and descriptive analysis techniques can be applied to the variables. In addition to the fact that the ratio scale does everything that a nominal, ordinal, and interval scale can do, it can also establish the value of absolute zero. The best examples of ratio scales are weight and height.

In market research, a ratio scale is used to calculate market share, annual sales, the price of an upcoming product, the number of consumers, etc.