Variance of Grouped Data

Theorem

Let $S$ be a set of grouped data.

Let it be assumed that $S$ approximates a Gaussian (normal) distribution

The variance of $S$ can be calculated by:

$(1): \quad$ assuming that the elements of $S$ are all at the mid-interval values

$(2): \quad$ subtracting Sheppard's correction of $\dfrac {h^2} {12}$, where $h$ is the bin width.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): grouped data
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): grouped data