Standard Deviation

Standard Deviation - 1 INTUITIVE REASONING(Offered in class...

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Unformatted text preview: 1. INTUITIVE REASONING (Offered in class) In classical statistics, the goal is always to estimate parameter from sample. When one collects a sample with n observations, the sample will have n pieces of information (in stats, this is known as Degrees of Freedom). Once we calculate the sample mean and use it in other estimations (in our case, we use the sample mean in the estimation of standard deviation), we don’t have n pieces of information anymore. Along with the sample mean, we have only n-1 pieces of information. That is why we use n-1 instead of n . Note: If you are happy with the above reasoning, you don’t have to know the below reasoning. 2. ANALYTICAL REASONING Claim: the average of squared deviations from Sample mean ≤ the average squared deviations from Population mean i.e. ∑ [¡ ¢ £¤¡̅] ¥ ¦ ¢§¨ ©ª« ¬ ∑ [¡ ¢ £ ¤­] ¥ ©ª« ¦ ¢§¨ i.e. the average of squared deviations from Sample mean underestimates the average of Squared deviations from Population mean. of Squared deviations from Population mean....
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This note was uploaded on 02/12/2012 for the course ECON 136 taught by Professor Johanek during the Spring '11 term at Boston Architectural.

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Standard Deviation - 1 INTUITIVE REASONING(Offered in class...

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