Grouped data

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data. There are two major types of grouping: data binning of a single-dimensional variable, replacing individual numbers by counts in bins; and grouping multi-dimensional variables by some of the dimensions (especially by independent variables), obtaining the distribution of ungrouped dimensions (especially the dependent variables).

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data. There are two major types of grouping: data binning of a single-dimensional variable, replacing individual numbers by counts in bins; and grouping multi-dimensional variables by some of the dimensions (especially by independent variables), obtaining the distribution of ungrouped dimensions (especially the dependent variables). \bar{x}=\frac{\sum{f\,x}}{\sum{f}} . In this formula, x refers to the midpoint of the class intervals, and f is the class frequency. Note that the result of this will be different from the sample mean of the ungrouped data. The mean for the grouped data in the above example, can be calculated as follows: Thus, the mean of the grouped data is \bar{x}=\frac{\sum{f\,x}}{\sum{f}} = \frac{405}{20} = 20.25 The mean for the grouped data in example 4 above can be calculated as follows: Thus, the mean of the grouped data is \bar{x}=\frac{\sum{f\,x}}{\sum{f}} = \frac{460}{40} = 11.5 ==See also== Aggregate data Censoring (statistics) Data binning Partition of a set Level of measurement Frequency distribution Discretization of continuous features ==References==

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