An anthropologist studying food gathering practices in three remote communities records daily caloric intake per person: Community X averages 2,100 kcal, Community Y averages 3,400 kcal, and Community Z averages 2,800 kcal. If she surveys 12 people from X, 8 from Y, and 10 from Z, what is the weighted average daily caloric intake across all 30 individuals?

["# Calculating the Weighted Average Daily Caloric Intake Across Remote Communities", "Understanding human health and adaptation in remote environments often depends on analyzing nutritional intake. Recently, a field anthropologist conducted a detailed study across three isolated communities, measuring daily caloric consumption to assess dietary patterns and their implications for survival and wellness.", "## The Three Communities and Their Diets", "The researcher studied:\n- Community X with an average intake of 2,100 kcal per person, based on interviews with 12 individuals.\n- Community Y exhibited a notably higher intake at an average of 3,400 kcal per person, derived from data collected from 8 people.\n- Community Z showed a moderate intake averaging 2,800 kcal per person, determined through surveys of 10 community members.", "Each community’s size and sampling represent a practical approach to gathering reliable initial data in hard-to-reach regions, ensuring diversity while maintaining scientific rigor.", "## What Is a Weighted Average?", "Because the communities vary in size—12 from X, 8 from Y, and 10 from Z—the simple arithmetic mean of 2,100, 3,400, and 2,800 would not reflect true dietary contribution from each group. Instead, a weighted average provides a more accurate picture by accounting for sample size.", "## Calculating the Weighted Average Daily Caloric Intake", "To compute the weighted average, we multiply each community’s average daily caloric intake by the number of surveyed individuals, sum these values, and divide by the total number of people surveyed.", "### Step-by-step calculation:", "- Community X: ( 12 \ imes 2,100 = 25,200 ) kcal\n- Community Y: ( 8 \ imes 3,400 = 27,200 ) kcal\n- Community Z: ( 10 \ imes 2,800 = 28,000 ) kcal", "Total caloric intake across all individuals:\n( 25,200 + 27,200 + 28,000 = 80,400 ) kcal", "Total number of individuals surveyed:\n( 12 + 8 + 10 = 30 )", "Weighted average daily caloric intake:\n[\n\frac{80,400}{30} = 2,680 \ ext{ kcal per person}\n]", "## Summary and Insights", "The weighted average daily caloric intake across the three remote communities is 2,680 kcal per person. This figure balances the modest intake of Community X with the higher consumption in Community Y, appropriately weighing each group by the number surveyed.", "Such calculations are vital in anthropological research, offering nuanced insight into nutrition, resource availability, and cultural behaviors. They help assess health outcomes, guide interventions, and deepen understanding of human adaptation in isolated settings.", "Whether studying ancient hunter-gatherers or modern subsistence populations, integrating sampling weights ensures scientific accuracy and meaningful interpretation. This method exemplifies how meticulous fieldwork and statistical rigor combine to illuminate the foundations of human survival and resilience."]