5G networks and beyond introduce a larger number of Network Elements (NEs) and functions than former cellular generations. The increase in NEs will, thus, result in significantly increasing the Management-Plane (M-Plane) data collected from the NEs. Therefore, the conventional centralized Network Management Systems (NMSs) will face fundamental challenges in processing the M-Plane data. In this paper, we present the concept of Quality of Monitoring (QoM) as a solution, which is able to reduce the M-Plane data already at the NEs. First, QoM aggregates the raw M-Plane data into Key Performance Indicators (KPIs). To these KPIs, the QoM applies a data-driven algorithm to define information loss limits for QoM classes specific for each KPI time series. Then, the QoM applies the classes for compressing the KPI data utilizing a lossy-compression method, which is a derivative of the Piece-Wise Constant Approximation (PWCA) algorithm. To evaluate the performance of the QoM solution, we use M-Plane raw data from a live LTE network and calculate four KPIs, while each KPI has different statistical characteristics. We also define three QoM classes named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Exact</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Optimized</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sharp</i> . For all KPIs, the class <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Optimized</i> has a higher compression rate than the class <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Exact</i> , while the class <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sharp</i> has the highest compression rate. Assuming that, for example, NEs of a network produce 280 MB of raw data containing information that needs to be transferred to the network operations center; we use KPIs to represent the information contents of the data, and QoM solution to transfer the data over the network. As a result, the QoM solution achieves an estimated 95% compression gain from the raw data in transfer.