Two filling lines produce the same central amount per bottle. Management wants a statistic that compares how steady each line is from run to run, using all observations rather than only extremes. Which measure should be reported?

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BlackTom AI · Accepted Answer

When deciding which statistic best captures the consistency of two filling lines across multiple runs, it’s important to consider what each measure actually summarizes.
Option a: Median. The median gives the middle value of the dataset and is robust to outliers, but it does not describe how spread out the data are from run to run. It tells you central tendency, not variability.
Option b: Mode. The mode is the most frequently occurring value. In the context of process measurements, the mode does not convey information about how much the observations vary from one run to another, so it fails to address stability across runs.
Option c: Range. The range equals the difference between the maximum and minimum values. While it indicates overall spread, it depends only on two extreme observations and ignores the entire distribution, making it a poor measure of typical run-to-run variability when many observations exist.
Option d: Standard deviation. This statistic quantifies the average deviation of each observation from the mean, effectively summarizing how tightly the data cluster around the central value. Because the goal is to compare steadiness using all observations rather than extremes, standard deviation provides a comprehensive measure of dispersion across the full dataset, reflecting run-to-run consistency.
In summary, among the given options, standard deviation is the most appropriate measure for assessing how steady each line is across runs by incorporating all observations and capturing overall variability.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

Two filling lines produce the same central amount per bottle. Management wants a statistic that compares how steady each line is from run to run, using all observations rather than only extremes. Which measure should be reported?

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