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Argue why the pooled estimator Sp is a weighted mean of S1 and S2, where S1...

Argue why the pooled estimator Sp is a weighted mean of S1 and S2, where S1 is the first sample sample standard deviation and S2 is the second sample sample standard deviation.

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Answer #1

The Pooled Standard Deviation is a weighted average of standard deviations for two or more groups. The individual standard deviations are averaged, with more “weight” given to larger sample sizes.

The weighting gives larger groups a proportionally greater effect on the overall estimate.

The pooled standard deviation is calculated by weighting the individual values of standard deviation with the size of the sample. Hence, the pooled estimator which is pooled standard deviation Sp is a weighted mean of   S1 and S2, where S1 is the first sample sample standard deviation and S2 is the second sample sample standard deviation.

Formula for pooled estimator Sp is given as :

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