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Encyclopedia > Descriptive statistics

Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. 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. It is necessary to be familiar with primary methods of describing data in order to understand phenomena and make intelligent decisions.[1] Various techniques that are commonly used are classified as: For other uses, see Data (disambiguation). ...

  • Graphical displays of the data in which graphs summarize the data or facilitate comparisons.
  • Tabular description in which tables of numbers summarize the data.
  • Summary statistics (single numbers) which summarize the data.

In general, statistical data can be briefly described as a list of subjects or units and the data associated with each of them. Although most research uses many data types for each unit, this introduction treats only the simplest case.


There may be two objectives for formulating a summary statistic:

  1. To choose a statistic that shows how different units seem similar. Statistical textbooks call one solution to this objective, a measure of central tendency.
  2. To choose another statistic that shows how they differ. This kind of statistic is often called a measure of statistical variability.

When summarizing a quantity like length or weight or age, it is common to answer the first question with the arithmetic mean, the median, or, in case of an unimodal distribution, the mode. Sometimes, we choose specific values from the cumulative distribution function called quantiles. A statistic (singular) is the result of applying a statistical algorithm to a set of data. ... In statistics, central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context. ... A statistic (singular) is the result of applying a statistical algorithm to a set of data. ... In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured. ... In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ... This article is about the statistical concept. ... In statistics, mode means the most frequent value assumed by a random variable, or occurring in a sampling of a random variable. ... In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a real-valued random variable, X. For every real number x, the cdf is given by where the right-hand side represents the probability that the random variable X takes on a value less than... This article or section does not cite any references or sources. ...


The most common measures of variability for quantitative data are the variance; its square root, the standard deviation; the range; interquartile range; and the average absolute deviation (average deviation). Quantitative data is data measured or identified on a numerical scale. ... This article is about mathematics. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of statistical dispersion of its values. ... In descriptive statistics, the range is the length of the smallest interval which contains all the data. ... In descriptive statistics, the interquartile range (IQR), also called the midspread and middle fifty is the range between the third and first quartiles and is a measure of statistical dispersion. ... The absolute deviation of an element of a data set is the absolute difference between that element and a given point. ...


When formulating a graphical display to summarise a dataset, the same two objectives may apply. A simple example of a graphical technique is a histogram, in which the central tendency and statistical variability can both be visualised. For the histograms usage in digital image processing, see Image histogram and Color histogram. ... In statistics, central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context. ... In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured. ...

Contents

Steps in descriptive statistics

  1. Collect data
  2. Classify data
  3. Summarize data
  4. Present data
  5. Proceed to inferential statistics if there are enough data to draw a conclusion.

In Christian liturgy, a collect is both a liturgical action and a short, general prayer. ... For Wikipedias categorization projects, see Wikipedia:Categorization. ... Statistical classification is a procedure in which individual items are placed into groups based on quantitative information on one or more characteristics inherent in the items (referred to as traits, variables, characters, etc) and based on a training set of previously labeled items. ... For other uses, see Presentation (disambiguation). ... It has been suggested that this article or section be merged with statistical inference. ... For other uses, see Data (disambiguation). ... A conclusion is a final proposition, which is arrived at after the consideration of evidence, arguments or premises. ...

Footnotes

  1. ^ Sternstein, Martin (1996). Statistics. Barrons, p. 1. ISBN 0-8120-9311-9. 

See also

The level of measurement of a variable in mathematics and statistics is a classification that was proposed in order to describe the nature of information contained within numbers assigned to objects and, therefore, within the variable. ... Statistical regularity is a notion in statistics that if we throw a thumbtack onto a table once, we would have a hard time predicting whether the point would touch the surface of the table or not. ... It has been suggested that this article or section be merged with inferential statistics. ... It has been suggested that this article or section be merged with statistical inference. ... In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate as much as possible as simply as possible. ... Data mining is the process of sorting through large amounts of data and picking out relevant information. ...

External links

This article is about the field of statistics. ... This article is about mathematical mean. ... In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ... The geometric mean of a collection of positive data is defined as the nth root of the product of all the members of the data set, where n is the number of members. ... In mathematics, the harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of average. ... This article is about the statistical concept. ... In statistics, mode means the most frequent value assumed by a random variable, or occurring in a sampling of a random variable. ... In descriptive statistics, the range is the length of the smallest interval which contains all the data. ... This article is about mathematics. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of statistical dispersion of its values. ... It has been suggested that this article or section be merged with inferential statistics. ... One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ... In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. ... The power of a statistical test is the probability that the test will reject a false null hypothesis (that it will not make a Type II error). ... In statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. ... In statistics, the Alternative Hypothesis is the hypothesis proposed to explain a statistically significant difference between results, that is if the Null Hypothesis has been rejected. ... Type I errors (or α error, or false positive) and type II errors (β error, or a false negative) are two terms used to describe statistical errors. ... The Z-test is a statistical test used in inference. ... A t-test is any statistical hypothesis test in which the test statistic has a Students t distribution if the null hypothesis is true. ... Maximum likelihood estimation (MLE) is a popular statistical method used for fitting a mathematical model to some data. ... Compares the various grading methods in a normal distribution. ... In statistical hypothesis testing, the p-value of a random variable T used as a test statistic is the probability that T will assume a value at least as extreme as the observed value tobserved, given that a null hypothesis being considered is true. ... In statistics, analysis of variance (ANOVA) is a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts. ... A meta-analysis is a statistical practice of combining the results of a number of studies. ... Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. ... The survival function, also known as a survivor function or reliability function, is a property of any random variable that maps a set of events, usually associated with mortality or failure of some system, onto time. ... The Kaplan-Meier estimator (also known as the Product Limit Estimator) estimates the survival function from life-time data. ... The logrank test (sometimes called the Mantel-Haenszel test or the Mantel-Cox test) [1] is a hypothesis test to compare the survival distributions of two samples. ... Failure rate is the frequency with which an engineered system or component fails, expressed for example in failures per hour. ... // Proportional hazards models are a sub-class of survival models in statistics. ... Several sets of (x, y) points, with the correlation coefficient of x and y for each set. ... In statistics, a spurious relationship (or, sometimes, spurious correlation) is a mathematical relationship in which two occurrences have no logical connection, yet it may be implied that they do, due to a certain third, unseen factor (referred to as a confounding factor or lurking variable). The spurious relationship gives an... In statistics, the Pearson product-moment correlation coefficient (sometimes known as the PMCC) (r) is a measure of the correlation of two variables X and Y measured on the same object or organism, that is, a measure of the tendency of the variables to increase or decrease together. ... In statistics, rank correlation is the study of relationships between different rankings on the same set of items. ... In statistics, Spearmans rank correlation coefficient, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a non-parametric measure of correlation – that is, it assesses how well an arbitrary monotonic function could describe the relationship between two variables, without making any assumptions about... The Kendall tau rank correlation coefficient (or simply the Kendall tau coefficient, Kendalls Ï„ or Tau test(s)) is used to measure the degree of correspondence between two rankings and assessing the significance of this correspondence. ... In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). ... In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xi, i = 1, ..., p, and a random term ε. The model can be written as Example of linear regression with one dependent and one independent variable. ... dataset with approximating polynomials Nonlinear regression in statistics is the problem of fitting a model to multidimensional x,y data, where f is a nonlinear function of x with parameters θ. In general, there is no algebraic expression for the best-fitting parameters, as there is in linear regression. ... Logistic regression is a statistical regression model for Bernoulli-distributed dependent variables. ...

  Results from FactBites:
 
Statistics - Conservapedia (1192 words)
Statistics analyzes data in two primary ways, the first is called descriptive statistics which describes and summarizes the data.
Statistics takes its name from the fact that it was traditionally taught to monarchs to enable them to manage affairs of state.
Frequentist approaches to inferential statistics primarily involve trying to compare descriptive statistics of two data sets to determine if they are significantly different.
Descriptive Statistics (1682 words)
Descriptive statistics are used to describe the basic features of the data in a study.
Descriptive statistics are typically distinguished from inferential statistics.
Descriptive Statistics are used to present quantitative descriptions in a manageable form.
  More results at FactBites »

 
 

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