Available with Image Analyst license.
Available with Spatial Analyst license.
Overview
Calculates statistics on the cells within a neighborhood around each cell of an input raster. Several shapes of neighborhood are available.
Notes
If the input raster is of floatingpoint type, only the Mean, Maximum, Median, Minimum, Percentile, Range, Standard Deviation, and Sum statistics are available.
When a circular, annulusshaped, or wedgeshaped neighborhood is specified, some of the outer diagonal cells may not be considered in the calculations since the center of the cell must be encompassed within the neighborhood.
Input NoData cells may receive a value in the output if the Ignore Nodata in Calculations option is checked, provided at least one cell within the neighborhood has a valid value.
For more information on this function, see the How Focal Statistics works topic.
Parameters
Parameter name  Description 

Raster (Required)  The input raster. 
Neighborhood  The shape of the area around each cell used to calculate the statistic. Each neighborhood has additional parameters with which to define the shape.
Note:For the Weight neighborhood type, only the Mean, Standard Deviation, or Sum statistics are supported. 
Statistics Type  Specifies the statistic type to be calculated.
The default statistic type is Mean. If the input raster is floating point, only the Mean, Maximum, Median, Minimum, Percentile, Range, Standard Deviation, and Sum statistic types are available. For Mean, Median, Percentile, and Standard Deviation, the output is always floating point. For Majority and Minority, if there is a tie between values with the highest (majority) or lowest (minority) frequency in the neighborhood, the processing cell location will receive the lowest of the tied values. If the value of the processing cell itself is one of the ties, that value will be returned instead. 
Ignore NoData in Calculations  Specifies whether NoData values are ignored by the statistic calculation.

Percentile Value  Specifies which percentile to calculate when Percentile is selected as the statistics type. The default is 90, for the 90th percentile. The values can range from 0 through 100. The 0th percentile is essentially equivalent to the Minimum statistic, and the 100th percentile is equivalent to Maximum, with the exception that the result will be floating point. A value of 50 will essentially produce the same result as the Median statistic. 
Kernel files
For the Irregular and Weight neighborhoods, you can save a custom kernel as a text file for later use.
After specifying the width and height, and entering the neighborhood values, use the Save As button to export it to an ASCII text file through the Save Neighborhood Kernel File dialog box. Use the Browse button to open the Input Neighborhood Kernel File dialog box to browse to and specify an existing kernel file to load.
The first line in the kernel file records the width and height of the kernel neighborhood in numbers of cells. The subsequent lines indicate how the input value that corresponds to that location in the kernel will be processed.
A value of 0 in the kernel file for either the irregular or the weight neighborhood type indicates the corresponding location will not be included in the calculation. For the irregular neighborhood, a value of 1 in the kernel file indicates that the corresponding input cell will be included in the operation. For the weight neighborhood, the value at each position indicates what the corresponding input cell value is to be multiplied by. Positive, negative, and decimal values are all valid options to use as a weight.