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The five-number summary gives information about the location (from the median), spread (from the quartiles) and range (from the sample minimum and maximum) of the observations. Since it reports order statistics (rather than, say, the mean) the five-number summary is appropriate for ordinal measurements, as well as interval and ratio measurements.
A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. [1]: 378
In statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample. [1] They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot.
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
The following may be applied to one-dimensional data. Depending on the circumstances, it may be appropriate to transform the data before calculating a central tendency. Examples are squaring the values or taking logarithms. Whether a transformation is appropriate and what it should be, depend heavily on the data being analyzed.
For example, if one test is performed at the 5% level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each conducted at the 5% level and all corresponding null hypotheses are true, the expected number of incorrect rejections (also known as false ...
In statistics, trend analysis often refers to techniques for extracting an underlying pattern of behavior in a time series which would otherwise be partly or nearly completely hidden by noise. If the trend can be assumed to be linear, trend analysis can be undertaken within a formal regression analysis , as described in Trend estimation .
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...