Big data refers to the large amount of information that is collected from different areas and shared on the internet. However, this development has led to difficulties in using frequent itemset mining applications. To overcome the issue of frequent data mining, this research has introduced an empirical sampling algorithm using RadeMacher average (ESA-RMA). When considering the size of the initial sample and scheduling the samples, the ESA utilizes the RadeMacher average to bound the samples. Initially, the data is obtained from the dataset of the human activity recognition (HAR) and real time datasets from smartphone gyroscope and accelerometer, then obtained data is pre-processed using the data normalization technique. Then, the ESA is used to select the labelled data and RMA is used to bound the samples. This bounding process defines the upper limit of the input data which helps in the effective mining of frequent item sets. Thus, the data with redundant items are mined out using the proposed ESA-RMA method. The experimental results show that the proposed ESA-RMA has taken a minimum run time of 212 ms for data obtained from smartphone accelerometer which is comparatively lower than the existing Scalable Simple Random Sampling (ScaSRS) with processing time of 362 ms. Similarly, for HAR dataset, the proposed method took processing time of 5.43 s whereas the existing vertical frequent time interval-related pattern (VertTIRP) mining approach took processing time of 7.82 s.