Editing Descriptive statistics (section)

==Use in statistical analysis==
Descriptive statistics provide simple summaries about the sample and about the observations that have been made. Such summaries may be either [[Quantitative research|quantitative]], i.e. [[summary statistics]], or visual, i.e. simple-to-understand graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.

For example, the shooting [[percentage]] in [[basketball]] is a descriptive statistic that summarizes the performance of a player or a team. This number is the number of shots made divided by the number of shots taken. For example, a player who shoots 33% is making approximately one shot in every three. The percentage summarizes or describes multiple discrete events. Consider also the [[grade point average]]. This single number describes the general performance of a student across the range of their course experiences.<ref name="trochim">{{cite web|last=Trochim|first=William M. K.|title=Descriptive statistics|url=http://www.socialresearchmethods.net/kb/statdesc.php|work=Research Methods Knowledge Base|access-date=14 March 2011|year=2006}}</ref>

The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of [[statistics]] appeared. More recently, a collection of summarisation techniques has been formulated under the heading of [[exploratory data analysis]]: an example of such a technique is the [[box plot]].

In the business world, descriptive statistics provides a useful summary of many types of data. For example, investors and brokers may use a historical account of return behaviour by performing empirical and analytical analyses on their investments in order to make better investing decisions in the future.

===Univariate analysis===
[[Univariate analysis]] involves describing the [[Frequency distribution|distribution]] of a single variable, including its central tendency (including the [[mean]], [[median]], and [[Mode (statistics)|mode]]) and dispersion (including the [[range (statistics)|range]] and [[quartiles]] of the data-set, and measures of spread such as the [[variance]] and [[standard deviation]]). The shape of the distribution may also be described via indices such as [[skewness]] and [[kurtosis]]. Characteristics of a variable's distribution may also be depicted in graphical or tabular format, including [[histograms]] and [[stem-and-leaf display]].

===Bivariate and multivariate analysis===

When a sample consists of more than one variable, descriptive statistics may be used to describe the relationship between pairs of variables. In this case, descriptive statistics include:

* [[Contingency table|Cross-tabulations]] and [[contingency tables]]
* Graphical representation via [[scatterplot]]s
* Quantitative measures of [[Correlation and dependence|dependence]]
* Descriptions of [[conditional distribution]]s

The main reason for differentiating univariate and bivariate analysis is that bivariate analysis is not only a simple descriptive analysis, but also it describes the relationship between two different variables.<ref>{{cite book |first=Earl R. |last=Babbie |title=The Practice of Social Research |url=https://archive.org/details/isbn_9780495598428 |url-access=registration |edition=12th |publisher=Wadsworth |year=2009 |isbn=978-0-495-59841-1 |pages=[https://archive.org/details/isbn_9780495598428/page/436 436–440] }}</ref> Quantitative measures of dependence include correlation (such as [[Pearson's r]] when both variables are continuous, or [[Spearman's rho]] if one or both are not) and [[covariance]] (which reflects the scale variables are measured on). The slope, in regression analysis, also reflects the relationship between variables. The unstandardised slope indicates the unit change in the criterion variable for a one unit change in the [[prediction|predictor]]. The standardised slope indicates this change in standardised ([[z-score]]) units. Highly skewed data are often transformed by taking logarithms. The use of logarithms makes graphs more symmetrical and look more similar to the [[normal distribution]], making them easier to interpret intuitively.<ref>{{cite book |first=Todd G. |last=Nick |chapter=Descriptive Statistics |title=Topics in Biostatistics |series=[[Methods in Molecular Biology]] |volume=404 |location=New York |publisher=Springer |year=2007 |pages=33–52 |isbn=978-1-58829-531-6 |doi=10.1007/978-1-59745-530-5_3 |pmid=18450044 }}</ref>{{rp|47}}