Category:Definitions/Sheppard's Corrections
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This category contains definitions related to Sheppard's Corrections.
Related results can be found in Category:Sheppard's Corrections.
Let $S$ be a set of grouped data.
Let it be assumed that $S$ obeys a Gaussian (normal) distribution.
When calculating the moments of $S$ using the mid-interval values, it is in general necessary to apply an adjustment to the calculated values.
This is called a Sheppard's correction, and it is subtracted from the calculated moment thus:
| \(\ds \hat \mu_2\) | \(=\) | \(\ds m_2 - \dfrac {h^2} {12}\) | ||||||||||||
| \(\ds \hat \mu_3\) | \(=\) | \(\ds m_3\) | ||||||||||||
| \(\ds \hat \mu_4\) | \(=\) | \(\ds m_4 - \dfrac {m_2} 2 + \dfrac {7 h^2} {240}\) |
where:
- $m_i$ is the $i$th moment calculated from the mid-interval values
- $\hat \mu_i$ is the adjusted value of the $i$th moment
- $h$ is the bin width.
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