Quantitative Geology ESC 2305 – M.Sc. Applied Geology Statistics Statistics is a branch of mathematics that deals with the study of collecting, analyzing, interpreting, presenting, and organizing data in a particular manner. Statistics is defined as the process of collection of data, classifying data, representing the data for easy interpretation, and further analysis of data. Statistics can be used to predict the future, determine the probability that a specific event will happen, or help answer questions about a survey. Different sectors such as psychology, sociology, geology, probability, and so on also use statistics to function. Importance of Statistics The important functions of statistics are: • Statistics helps in gathering information about the appropriate quantitative data. • It depicts the complex data in graphical form, tabular form and in diagrammatic representation to understand it easily. • It provides the exact description and a better understanding. • It helps in designing the effective and proper planning of the statistical inquiry in any field. • It gives valid inferences with the reliability measures about the population parameters from the sample data. • It helps to understand the variability pattern through the quantitative observations. Scope of Statistics Statistics and Economics Statistical data and technique of statistical analysis have proved immensely useful in solving variety of economic problems, such as wages, prices, analysis of time series and demand analysis. It has also facilitated the development of economic theory. Wide applications of mathematics and statistics in the study of economics have led to the development of new disciplines called Economic Statistics and Econometrics. Scope of Statistics Statistics and Business The success of a businessman more or less depends upon the accuracy and precision of his statistical forecasting. The formation of a production plan in advance is a must which cannot be done without having quantitative facts about the products. Most of the large industrial and commercial enterprises are employing trained and efficient statisticians. Scope of Statistics Statistics and Industry In industry, Statistics is widely used in ‘Quality Control’. In production engineering, to find whether the product is conforming to specifications or not, statistical tools, which is inspection of plans, control charts etc. are of extreme importance. In inspections plans we have to resort to some kind of sampling – a very important aspect of Statistics. Scope of Statistics Statistics and Biology The association between statistical methods and biological theories was first studied by Francis Galton in his work in ‘Regression’. According to Karl Pearson, the whole ‘theory of heredity’ rests on statistical basis. Scope of Statistics Statistics and Astronomy In astronomy, the theory of Gaussian ‘Normal Law of Errors’ for the study of the movement of stars and planets is developed using the ‘Principle of Least Squares’. Scope of Statistics Statistics and Medical Science The statistical tools for the collection, presentation and analysis of observed facts relating to the causes and incidence of diseases and the results obtained from the use of various drugs and medicines are of great importance. Moreover, the efficacy of a manufactured drug or injection or medicine is tested by using the ‘tests of significance’ – (t-test). Limitations of Statistics ▪ Statistics is not suited to the study of qualitative phenomenon. ▪ Statistics does not study individuals. ▪ Statistical laws are not exact. ▪ Results are true only on average. ▪ Statistics is liable to be misused. Geostatistics Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture. Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS). Population and Sample Population A population refers to any collection of specified group of human beings or of nonhuman entities such as objects, educational institutions, time units, geographical areas, prices of wheat or salaries drawn by individuals. Types of Population 1. Finite Population 2. Infinite Population 3. Existent Population 4. Hypothetical Population Types of Population Finite Population The finite population is also known as a countable population in which the population can be counted. In other words, it is defined as the population of all the individuals or objects that are finite. Examples: ▪ Employees of a company ▪ The books in a library ▪ Potential consumer in a market Types of Population Infinite Population The infinite population is also known as an uncountable population in which the counting of units in the population is not possible. Examples: ▪ The population of pressures at various points in the atmosphere. ▪ The number of germs in the patient’s body. Types of Population Existent Population The existing population is defined as the population of concrete individuals. In other words, the population whose unit is available in solid form is known as existent population. Examples are books, students etc. Types of Population Hypothetical Population The population in which whose unit is not available in solid form is known as the hypothetical population. A population consists of sets of observations, objects etc. that are all something in common. Examples are an outcome of rolling the dice, the outcome of tossing a coin. Sample A selected group of some elements from the totality of the population is known as the sample. The process of selecting a sample from the population is called Sampling. For example, some people living in India is the sample of the population. Types of Sampling Basically, there are two types of sampling. They are: • Probability sampling • Non-probability sampling Types of Sampling Probability Sampling In probability sampling, the units of the population are not selected at the discretion of the researcher, but by means of certain procedures which ensure that every unit of a population has one fixed probability of being included in the sample. Types of Sampling Non-Probability Sampling In non-probability sampling, the population units can be selected at the discretion of the researcher. Those samples will use the human judgements for selecting units and has no theoretical basis for estimating the characteristics of the population. Variables A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, gender, business income and expenses, country of birth, capital expenditure, class grades, eye color and vehicle type are examples of variables. It is called a variable because the value may vary between data units in a population, and may change in value over time. For example; 'income' is a variable that can vary between data units in a population (i.e. the people or businesses being studied may not have the same incomes) and can also vary over time for each data unit (i.e. income can go up or down). Types of Variables ▪ Numeric Variables ▪ Categorical Variables Types of Variables Numeric Variables Numeric variables have values that describe a measurable quantity as a number, like 'how many' or 'how much'. Therefore numeric variables are quantitative variables. Types of Numeric Variables are: ▪ Continuous Variables ▪ Discrete Variables Types of Variables Continuous Variables Observations can take any value between a certain set of real numbers. Examples of continuous variables include height, time, age, and temperature. Discrete Variables Observations can take a value based on a count from a set of distinct whole values. A discrete variable cannot take the value of a fraction between one value and the next closest value. Examples of discrete variables include the number of registered cars, number of business locations, and number of children in a family, all of which measured as whole units. Types of Variables Categorical Variables Categorical variables have values that describe a 'quality' or 'characteristic' of a data unit, like 'what type' or 'which category’. Categorical variables are qualitative variables and tend to be represented by a non-numeric value. Types of Categorical Variables are: ▪ Ordinary Variable ▪ Nominal Variable Types of Variables Ordinary Variable Observations can take a value that can be logically ordered or ranked. The categories associated with ordinal variables can be ranked higher or lower than another. Examples of ordinal categorical variables include academic grades (i.e. A, B, C), clothing size (i.e. small, medium, large, extra large) and attitudes (i.e. strongly agree, agree, disagree, strongly disagree). Types of Variables Nominal Variable Observations can take a value that is not able to be organized in a logical sequence. Examples of nominal categorical variables include gender, business type, eye color, religion and brand. Types of Variables
