The heterogeneous nature of soil is an important consideration when measuring or predicting soil properties. The purpose
of this study was to describe the spatial pattern and its varying rule of penetration resistance (PR). The PR was measured for fields with and without intense grazing on Chestnut soils (CS) on Inner Mongolia Plateau for Typic
Chestnut soil (TCS), Dark Chestnut Soil (DCS), and Sandy Chestnut Soil (SCS) by soil hardness tester of Fuji Wara. Also PR was measured on DCS and SCS fields for post grazing. The varying rule of soil PR was inferred by the law of statistics based on the relation of Standard Deviation (SD) and the Mean (M) of PR and the relationship of PR of different fields. There were large differences between the average PR of different fields of a soil but small variations in coefficient of variation (CV). The PR of a field has changed for the change of grazed situation, its extreme value, middle value, the distributed range of the measured PR and SD are all changed the same ratio as that of M. Pooled across fields, the within-field Ms were extremely significantly correlated with SD. The autocorrelation length for both conventional and compacted TCS was around 2.3 m in the north-south direction, and was around 1 m for conventional SCS and 2 m for compacted SCS. There was no significant autocorrelation length for the other fields. And the
distribution pattern of PR is normal distribution and it did not change with the PR. Based on these results and the law of expected value and variance we can concluded that the SD has changed almost the same time as that of M and the PR difference between two points will vary the same ratio as their M after being disturbed. This was caused by the features of ratio variation and co-ratio variation of PR of different point. The co-ratio variation is the determining factor for the rank (order) stability and spatial distribution pattern.