Tennessee Wastewater Operator Practice Exam

Which of the following is a method for grouping measurements and summarizing results?

1. Variance

2. Arithmetic mean

3. Standard error

4. Range

The correct answer is: Arithmetic mean

The arithmetic mean is a foundational method for grouping measurements and summarizing results in statistical analysis. It is calculated by adding together all the values of a dataset and then dividing that sum by the number of values. This provides a single typical value that represents the data set, making it easy to understand the central tendency of the measurements. The arithmetic mean is widely used because it is straightforward to compute and interpret, providing a quick insight into the average of the data points collected. In the context of the other options, variance measures the degree of spread in a dataset, indicating how far individual measurements are from the mean. Although it provides valuable information about data variability, it does not summarize the data in a single representative value like the mean does. The standard error reflects the accuracy of the mean as an estimate of the population mean, but it also does not summarize all measurements effectively on its own. The range simply provides the difference between the highest and lowest values in a dataset, giving insight into the spread but not summarizing the data in a complete or average sense. Therefore, the arithmetic mean stands out as the best method for grouping and summarizing measurements.