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Important one liner (Average)
- An average (mean) summarizes a set of numbers by dividing their total by the count of values.
- An outlier can significantly shift the average, so median may be more representative in skewed distributions.
- In data analysis, the arithmetic mean is sensitive to every value and is useful for normally distributed data.
- Weighted averages assign different importance to values by using weights in the summation.
- Geometric mean is used for rates of change, like growth rates, by multiplying values and taking the root.
- Harmonic mean applies when averaging ratios or speeds; it’s the reciprocal of the arithmetic mean of reciprocals.
- Moving average smooths time series data by computing the mean of fixed-length subsets sequentially.
- Simple average treats all data points equally, while trimmed mean excludes extremes before averaging to reduce outlier impact.
- Running average updates the mean incrementally as new data arrives without recomputing from scratch.
- Combined average merges means of two groups: total sum divided by total count across both groups.
- Root mean square (quadratic mean) emphasizes larger values and is used in physics and engineering calculations.
- Average deviation measures dispersion by computing mean of absolute differences from the mean.
- Group average calculates the mean per subgroup, then averages subgroup means, useful in stratified datasets.
- Average speed differs from overall distance/time average when varied speeds are over equal distances.
- In finance, the average return is computed as arithmetic mean, though geometric mean gives compounded return.
- Average salary reflects central tendency but can hide income inequality within the dataset.
- Exam average reflects overall performance but does not indicate range or distribution of scores.
- Collaborative filtering uses average ratings from users to recommend items in recommender systems.
- Grade point average (GPA) is a weighted average of course grades, with credits as weights.
- Average life expectancy is influenced by infant mortality; cohort-based averages give detailed insights.
- Average cost analysis helps in budgeting by summing expenses and dividing by the number of units or periods.
- In manufacturing, average defect rate tracks quality by dividing defective units by total produced units.
- Average calories per serving aids nutrition planning by totaling calories and dividing by servings.
- Average fill level in tanks informs maintenance schedules by tracking mean volumes over time.
- In traffic flow, average vehicle speed and density assess congestion levels on road segments.
- Average torque in rotating machinery helps predict performance and load distribution.
- National average rainfall indicates climate patterns and informs water resource management.
- Average daily temperature smooths variation to understand seasonal trends in meteorology.
- Average pixel intensity summarizes image brightness in digital image processing.
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