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Also known as: Average, Expected Value
Arithmetic average of dataset values, measuring central tendency.
DESCRIPTION
The mean is a foundational statistic representing the average value of a dataset, computed as the sum divided by the count. It is widely used to summarize continuous data and for parameter estimation in statistical models. Means are sensitive to outliers and skewed distributions, which can distort interpretation. Alternatives like the median or trimmed mean may provide more robust summaries under heavy-tailed or skewed conditions. The mean underpins many algorithms and tests, including least squares regression and ANOVA. In probability, the expected value generalizes the mean to random variables. Weighted means account for varying importance of observations. Streaming and distributed systems often compute means incrementally for scalability.
ALTERNATIVE DEFINITIONS
Encyclopaedia Britannica
In mathematics and statistics, the arithmetic mean is the sum of the values divided by the number of values.
Provides a concise, arithmetic-focused definition for general audiences.
Wikipedia
In mathematics and statistics, the arithmetic mean (or simply the mean or average) of a set of numbers is the sum of the numbers divided by the count of numbers in the set.
Highlights common synonyms and the general computational rule.
RELATED TERMS
Variance Standard Deviation Geometric Mean Harmonic Mean Trimmed Mean Outliers Normal Distribution
COMPETING TERMS
RELATIONS
- Narrower: Geometric Mean Harmonic Mean Trimmed Mean
KNOWLEDGE AREAS
Mathematics Data Science Data Visualization
TARGET AUDIENCE
Data Scientist Data Analyst BI Specialist Analytics Engineer Data Engineer
EXTERNAL SOURCES
- Wikipedia - Arithmetic mean
- Penn State STAT Online - Course explanation of sample mean
- NIST Engineering Statistics Handbook - NIST reference on means
- NumPy - NumPy mean function documentation
TOP QUESTIONS
When should you use the Mean instead of the Median?
Use the mean when data are roughly symmetric without extreme outliers. The mean captures overall magnitude and supports many statistical models. For skewed distributions, the median is often more robust.
Category: Requirements
Why is the Mean sensitive to outliers?
Each value contributes linearly to the sum, so extreme values disproportionately shift the average. This sensitivity can misrepresent the central location in heavy-tailed or contaminated data.
Category: Risks
How is the Mean used in machine learning?
Means underpin loss functions (e.g., MSE uses squared deviations from the mean) and parameter estimation. They also serve in normalization and feature scaling.
Category: Application
What is the difference between Mean and Expected Value?
The mean typically refers to a sample average, while expected value is the theoretical average of a random variable. The sample mean estimates the expected value under IID assumptions.
Category: Misunderstanding
How do you compute a streaming Mean efficiently?
Use incremental formulas that update the mean with each new observation without storing all data. Welford’s method also tracks variance numerically stably.
Category: Best practices
What are robust alternatives to the Mean?
The median, trimmed mean, and Winsorized mean reduce sensitivity to outliers. These alternatives trade some efficiency for robustness under contamination.
Category: Alternatives
How does sample size affect the Mean’s reliability?
Larger samples typically yield a mean with lower standard error, improving precision. Small samples are more volatile and susceptible to outliers.
Category: Requirements
Is the Mean appropriate for ordinal data?
No. The mean assumes interval-scale properties. For ordinal data, the median or mode is more appropriate.
Category: Mistakes
What is a common misuse of the Mean in reporting?
Reporting the mean for highly skewed income or response-time data can mislead. Pair it with median and dispersion to provide context.
Category: Mistakes