#### 18.0A linguist analyzing historical texts uses a language model to compute semantic drift over time, measuring change in word usage frequency across 5 decades. The model assigns drift scores: 0.8, 1.2, 1.5, 0.9, and 1.6. What is the mean absolute deviation of these drift scores from the mean?

["Linguistic Insight: Understanding Semantic Drift with Statistical Precision", "In the evolving landscape of language, researchers are increasingly turning to computational tools to quantify subtle shifts in meaning—a phenomenon known as semantic drift. A recent study examines how word usage frequencies change across five decades, leveraging advanced language models to compute drift scores. By analyzing five key drift metrics—0.8, 1.2, 1.5, 0.9, and 1.6—the analysis reveals significant fluctuations in lexical evolution. But beyond reporting raw scores, understanding their variability is crucial: scientists often turn to mean absolute deviation (MAD) to assess consistency and reliability in semantic change measurements.", "### What Is Mean Absolute Deviation?", "Mean Absolute Deviation (MAD) quantifies the average distance between individual data points and the mean of the dataset. Unlike standard deviation, MAD uses absolute values, avoiding signs and providing a clear, intuitive measure of dispersion. It is especially useful when dealing with real-world linguistic data that may contain outliers or non-normal distributions.", "For the given drift scores—0.8, 1.2, 1.5, 0.9, and 1.6—we compute the mean first:", "[\n\ ext{Mean} = \frac{0.8 + 1.2 + 1.5 + 0.9 + 1.6}{5} = \frac{6.0}{5} = 1.2\n]", "Next, calculate the absolute deviation of each score from the mean:", "- |0.8 − 1.2| = 0.4\n- |1.2 − 1.2| = 0.0\n- |1.5 − 1.2| = 0.3\n- |0.9 − 1.2| = 0.3\n- |1.6 − 1.2| = 0.4", "Sum these deviations:", "[\n0.4 + 0.0 + 0.3 + 0.3 + 0.4 = 1.4\n]", "Finally, divide by the number of observations (5) to find the mean absolute deviation:", "[\n\ ext{MAD} = \frac{1.4}{5} = 0.28\n]", "### Interpreting Drift Through Statistical Lenses", "The MAD of 0.28 reflects moderate variability in semantic drift scores across the five decades. This indicates that while word meanings exhibit clear shifts—evidenced by scores above the baseline mean of 1.2—these changes are fairly consistent in magnitude, enabling researchers to detect meaningful trends without overwaving to noise.", "This computational approach empowers linguists to move beyond qualitative descriptions of meaning change, offering statistical rigor to historical textual analysis. As language continues to evolve in digital eras, tools like MAD help decode the rhythm of semantic drift, turning fleeting linguistic shifts into measurable, interpretable patterns.", "### Conclusion", "Mapping semantic drift is not just a lexical curiosity—it’s a window into cultural and cognitive change. By computing the mean absolute deviation of drift scores, researchers ensure their findings are both precise and reproducible. In the intersection of linguistics and computational modeling, statistics like MAD transform abstract linguistic evolution into actionable data.", "---", "Keywords: semantic drift, language evolution, computational linguistics, mean absolute deviation, historical texts, word usage frequency, language model analysis, historical semantics."]