Glossary
Mean
The mean, or arithmetic mean, is the sum of all values in a dataset divided by the number of observations. It is the most common measure of central tendency and represents the "average" value around which the data are distributed.
Definition
The mean, or arithmetic mean, is the sum of all values in a dataset divided by the number of observations. It is the most common measure of central tendency and represents the "average" value around which the data are distributed.
Why It Matters
The mean is the default summary statistic in virtually every field of research because it uses all available data points and has desirable mathematical properties for inference. It is the foundation of the t-test, ANOVA, regression, and the Central Limit Theorem. However, because it is sensitive to extreme values, it may misrepresent the centre of skewed distributions.
Example
A company reports that the mean salary among its 100 employees is £55,000. This figure is mathematically correct, but if the CEO earns £500,000 while most staff earn £30,000, the mean is pulled upward and does not reflect the typical employee's experience. In such cases, the median provides a more robust measure of central tendency.
Related Terms
Software Notes
- SPSS: Analyze > Descriptive Statistics > Frequencies or Descriptives. Check "Mean" under the Statistics button.
- R:
mean(x, na.rm = TRUE). For grouped data:aggregate(y ~ group, data = df, mean). - Stata:
summarize varname, detailreturns the mean among other descriptive statistics.mean y, over(group)computes group means with survey-standard errors.