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The best tool to display stability of nosocomial infection rates over time is a

  1. Control chart

  2. Histogram

  3. Pareto chart

  4. Run chart

The correct answer is: Control chart

A control chart is the best tool to display stability of nosocomial infection rates over time. Control charts provide a visual representation of how a process is performing over time by plotting data points in relation to control limits. By analyzing the patterns on the chart, healthcare professionals can determine if the infection rates are stable or if there are any trends, shifts, or outliers indicating variation in the process. This tool is essential for monitoring the effectiveness of infection control measures and identifying any areas for improvement. The other options, such as histogram, Pareto chart, and run chart, are useful for different purposes but are not specifically designed to display the stability of infection rates over time as effectively as a control chart.