Lecture VI

Statistics

Lecture questions

Mathematical statistics Sampling Statistical population and sample Descriptive statistics

Definition of Statistics

• Statistics is the study of the collection, organization, analysis, interpretation, and presentation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of experiments.

• Mathematical statistics is the study of statistics from a mathematical standpoint.

Data analysis

• descriptive statistics - the part of statistics that describes data, i.e. summarises the data and their typical properties.

• inferential statistics - the part of statistics that draws conclusions from data (using some model for the data). It uses mathematical probabilities, make generalizations about a large group based on data collected from a small sample of that group.

Sampling

• In statistics, sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.

• The advantages of sampling are 1.the cost is lower2.data collection is faster3.since the data set is smaller it is possible to

ensure homogeneity and to improve the accuracy and quality of the data.

Statistical population and sample

• A statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. (N is population size).

• A sample is a subset of a population. n is sample size.

Sampling process stages• Defining the population of concern• Specifying a sampling method for selecting

items or events from the frame• Determining the sample size• Implementing the sampling plan• Sampling and data collecting

Properties of a “good” sample• Adequate sample size (statistical power)• Random selection (representative)

Sampling methods • Probability methodsa.random samplingb.systematic samplingc.stratified sampling• Nonprobability methodsa.Cluster sample.b.Convenience sample. The advantage of probability sampling is that

sampling error can be calculated.

Simple random sample• simple random sample is a subset of

individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals[1]. This process and technique is known as simple random sampling

Thank you for your attention !