Sheppard’s Corrections for Moments - why this is needed?
Grouping error: The error occurred due to the assumption that the frequencies are uniformaly distributed with the class intervals.
To have a lesser error, the distribution within a class should be:
1. Symmetrical
2. About the mid-point of the class interval
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Conditions for applying Sheppard’s Corrections for Moments:
1. Observations should relate to continuous variable.
2. Frequency curve of the distributions should be continuous.
3. The class frequencies should decrease towards the two ends of the range smoothly and gradually.
4. The class intervals should not be too small i.e., class count should not be large. Generally, minimum total frequency is 1000 and maximum class count is 20.
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Three types of moments are:
1. Moments about arbitrary point 2. Moments about origin 3. Moments about mean
A Moment about Origin is a special case of a Moment about an arbitrary point where the arbitrary point is set to origin 0.
Moments about Mean (also called Central moments)
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Why Moments are important?
a. Describe the characteristic of a distribution
b. Represent a convenient and unifying method for summarizing several statistical measures such as measures of tendency, variation, skewness and kurtosis.
00:00 Arithmetic mean for grouped data
00:38 Moments for grouped data
01:38 Reason for considering mid-point
03:12 What is Grouping error
05:42 Effect of distribution on grouping error
06:20 Sheppard's corrections
08:05 Conditions for Sheppard's corrections
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