Expected value is the weighted average outcome of a random variable.
E(X) = Σ[x × P(x)].
Variance = Σ[(x − E(X))² × P(x)].
Reach for this tool when characterising data for research, quality control, or business analysis. The results follow standard statistical definitions and are compatible with further inferential analysis.
Many users interpret statistical results without considering the distribution of the data. Standard deviation is most meaningful for roughly normally distributed data — in highly skewed datasets, the median and IQR are more appropriate measures of centre and spread.
A teacher calculates the class average and standard deviation for an exam: mean 64%, SD 18%. The high SD suggests a wide spread of performance levels — indicating the class may need differentiated support rather than a single revision strategy.
The expected value is the long-run average outcome if an experiment is repeated many times.
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