They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.
Overview[ edit ] In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal".
Ideally, statisticians compile data about the entire population an operation called census. This may be organized by governmental statistical institutes.
Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data types like incomewhile frequency and percentage are more useful in terms of describing categorical data like race.
When a census is not feasible, a chosen subset of the population called a sample is studied.
Once a sample that is representative Meaning of descriptive statistics the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data. However, the drawing of the sample has been subject to an element of randomness, hence the established numerical descriptors from the sample are also due to uncertainty.
To still draw meaningful conclusions about the entire population, inferential statistics is needed. It uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.
These inferences may take the form of: Inference can extend to forecastingprediction and estimation of unobserved values either in or associated with the population being studied; it can include extrapolation and interpolation of time series or spatial dataand can also include data mining.
Sampling[ edit ] When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models.
The idea of making inferences based on sampled data began around the mids in connection with estimating populations and developing precursors of life insurance. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole.
A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures.
There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.
Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.
The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method.
The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples.
Statistical inference, however, moves in the opposite direction— inductively inferring from samples to the parameters of a larger or total population. Experimental and observational studies[ edit ] A common goal for a statistical research project is to investigate causalityand in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables.
There are two major types of causal statistical studies: In both types of studies, the effect of differences of an independent variable or variables on the behavior of the dependent variable are observed.
The difference between the two types lies in how the study is actually conducted.Descriptive statistics are numbers that are used to summarize and describe data.
The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. Descriptive statistics is a set of brief descriptive coefficients that summarizes a given data set representative of an entire or sample population.
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
1. Branch of mathematics concerned with collection, classification, analysis, and interpretation of numerical facts, for drawing inferences on the basis of their quantifiable likelihood (probability).
Statistics can interpret aggregates of data too large to be intelligible by ordinary observation because such data (unlike individual quantities) tend to behave in regular, predictable manner.
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Descriptive statistics Dr. C. George Boeree If you have a large number of measurements, the best thing you can do is to make a graph with all the possible scores along the bottom (x axis), and the number of times you came across that score recorded vertically (y axis) in the form of a bar.